Naeem Saleem

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• PhD-Mathematics
• Professor (Associate) at University of Management and Technology

This article contain the concepts of fuzzy (α − η) and fuzzy (β − ψ)−generalized proximal contractive mappings in the setup of b−fuzzy metric spaces. We proved the existence of coincidence and best proximity points of fuzzy (α − η)− and fuzzy (β − ψ)−generalized proximal contractions on b−fuzzy metric spaces. Some nontrivial examples are provided t...

In this article, we provided fixed‐point results for (Θ,G1)$$ \left(\Theta, {G}_1\right) $$‐quasirational contraction and (Θ,G2)$$ \left(\Theta, {G}_2\right) $$‐quasirational contraction within the setting of triple controlled metric‐like spaces. Furthermore, we demonstrate that this extension of spaces does not constitute a Hausdorff space. Our re...

A modified Halpern-type iterative technique, having weak and strong convergence results for approximating invariant points of a new class of enriched nonspreading operators subject to some standard mild conditions in the setting of real Banach spaces, was presented in this work. It was demonstrated with an example that the class of enriched nonspre...

The goal of this work is to establish ℑ-contractions and to show some novel fixed point theorems for these contractive conditions in the setting of generalized metric spaces in the sense of Jleli and Samet. Finally, using proven fixed point results, an existence result for a solution of the RLC circuit’s current differential equation is established...

In this article, we define a new class of noncommuting self mappings known as the S-operator pair. Also, we provide the existence and uniqueness of common fixed point results involving the S-operator pair satisfying the (F,φ,ψ,Z)-contractive condition in m-metric spaces, which unifies and generalizes most of the existing relevant fixed point theore...

In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular b−metric space and rectangular b−metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples a...

This study presents an innovative iterative method designed to approximate common fixed points of generalized contractive mappings. We provide theorems that confirm the convergence and stability of the proposed iteration scheme, further illustrated through examples and visual demonstrations. Moreover, we apply s-convexity to the iteration procedure...

Our study presents a novel orbit with s−convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for u , α , β ∈ C and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with num...

Krasnoselskii’s iteration is a classical and important method for approximating the fixed point of an operator that satisfies certain conditions. Many authors have used this approach to obtain several famous fixed point theorems for different types of operators. It is well known that Kirk’s iteration can be seen as a generalization of Krasnoselskii...

The aim of this paper is to obtain a fractal set of −iteratedfunctionsystemscomprisinggeneralized-contractions. For a variety of Hutchinson–Wardowski contractive operators, we prove that this kind of system admits a unique common attractor. Consequently, diverse outcomes are obtained for generalized iterated function systems satisfying various gene...

In the context of $b$-metric spaces, this paper introduces two concepts: admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and pairwise admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and establishes criteria for intuitionistic fuzzy fixed points under such contractions. It is demonstrated that a pair of set-valued...

In uniformly convex Banach spaces, we study within this research Fibonacci–Ishikawa iteration for monotone asymptotically nonexpansive mappings. In addition to demonstrating strong convergence, we establish weak convergence result of the Fibonacci–Ishikawa sequence that generalizes many results in the literature. If the norm of the space is monoton...

The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair o...

In this chapter, we extend Wardowski’s idea of F-contraction by introducing the dual F-Suzuki type contraction and the triple F-Suzuki type contraction. We prove some fixed point theorems related to these contractions. Further, we apply our obtained results to find the existence of a solution to an integral equation.

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide...

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document}-con...

In this manuscript, we use the concept of multidimensional fixed point in a generalized space, namely, C-distance space with some nonlinear contraction conditions, such as Jaggi- and Dass-Gupta-type contractions. We provide results with a Jaggi-type hybrid contraction for the mentioned space. Moreover, we use control functions to get the desired re...

Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen...

Citation: Liu, X.; Zhou, M.; Hojat Ansari, A.; Saleem, N.; Jain, M.K. Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application. Mathematics 2024, 12, 121. Abstract: In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contraction...

In this paper, firstly, we introduce a method for finding common fixed point of L -Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and L -Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness princip...

In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the Sb-metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works...

In this research article, we have proved strong and ∆-convergence results for mapping satisfying (RCSC) condition via M-iteration process in CAT(0) spaces. Numerical examples are provided to show the superiority of our results over other existing results and to illustrate the faster convergence of the M iterative scheme as compared to many well-kno...

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra...

This paper designates two important properties of the existence–uniqueness of the mild solution for a fractional controlled fuzzy evolution equation involving the Caputo-derivative by using nonlocal conditions, where β ∈ (1, 2), and it is formulated as  c0 Dβ ωu(ω) = Au(ω) + χ(ω, u(h(ω))) + Q(ω)H(ω), u(0) = u0 + (−1)g(u), u′(0) = u1, where A...

This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define op...

In this manuscript, we establish the notion of neutrosophic rectangular extended b-metric spaces and derive some fixed point results for contraction mappings. Also, we provide several non-trivial examples. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to non-...

This article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergence of the iteration toward a fixed point of a specific mapping satisfying the condition (E) is obtained under some possible mild assumptions. It is worth mentioning that the iteration process JK...

Fuzzy graphs have many applications not only in mathematics but also in any field of science where the concept of fuzziness is involved. The notion of fuzziness is suitable in any environment, which favor to predicts the problem and solve this problem in a decent way. As compared to crisp theory, fuzzy graphs are a more beneficial and powerful tool...

The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an α−θ−Geraghty–Pat...

In this article, we introduce the concept of multivalued fractals in neutrosophic metric spaces using an iterated multifunction system made up of a finite number of neutrosophic B-contractions and neutrosophic Edelstein contractions. Further, we show that multivalued fractals exist and are unique in both complete neutrosophic metric spaces and comp...

The purpose of this paper is to define the notion of extended convex F contraction by imposing less conditions on the function F satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability o...

In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy b−rectangular and fuzzy rectangular metric like spaces. Various examples are g...

This study aims to provide some new classes of (a, b, F*)-weak Geraghty contraction and (a, b, F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition,...

In this paper, we introduce three classes of proximal contractions that are called the proximally λ − ψ−dominated contractions, generalized η γ β −proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F −metric spaces. Further, we obtain the best...

In this paper, we explore some extensions of multiple fixed point results for various distance spaces such as s-distance space, (s,q)-distance space, and balanced distance space. Some examples are also discussed for the elaboration of these generalized structures. An application of our result that demonstrates the existence of a unique solution of...

In this paper, we introduce two new concepts of F-contraction, called dual F∗-weak contraction and triple F∗-weak contraction, which generalize the existing contractions in the sense of Wardowski, Jleli and Samet as well as Skof. These new generalizations embed their roots in the aim devoted to extending the generalized Banach contraction conjunctu...

As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is prese...

In this article, we establish the concept of intuitionistic fuzzy double-controlled metric-like spaces by "assuming that the self-distance may not be zero"; if the value of the metric is zero, then it has to be "a self-distance". We derive numerous fixed-point results for contraction mappings. In addition, we provide several non-trivial examples wi...

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P-property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed poin...

In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the "sum conditions" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to som...

In this paper, an iterative scheme for finding common solutions of the set of fixed points for a pair of asymptotically quasi-nonexpansive mapping and the set of minimizers for the minimization problem is constructed. Using the idea of the jointly demicloseness principle, strong convergence results are achieved without imposing any compactness cond...

In this manuscript, our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces. We establish some fixed point theorems in this setting. Also, we plot some graphs of an example of obtained result for better understanding. We use the concepts of continuous triangular norms and continuous triangular conorms in an intuiti...

In this paper, we establish the concept of controlled neutrosophic metric-like spaces as a generalization of neutrosophic metric spaces and provide several non-trivial examples to show the spuriousness of the new concept in the existing literature. Furthermore, we prove several fixed point results for contraction mappings and provide the examples w...

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify Fcontraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-li...

In this manuscript, we establish a novel class of nonlinear mappings called β-enriched Suzuki generalized multivalued non-expansive mappings and prove a new existence of common fixed points for a commuting pair comprising an enriched single-valued and an enriched multivalued mapping both satisfying condition (C) in the setup of a uniformly convex B...

Soft set theory has evolved to provide a set of valuable tools for dealing with ambiguity and uncertainty in a variety of data structures related to real-world challenges. A soft set is characterized via a multivalued function of a set of parameters with certain conditions. In this study, we relax some conditions on the set of parameters and genera...

In this article, we introduce the notions of extended b -rectangular and controlled rectangular fuzzy metric-like spaces that generalize many fuzzy metric spaces in the literature. We give examples to justify our newly defined fuzzy metric-like spaces and prove that these spaces are not Hausdorff. We use fuzzy contraction and prove Banach fixed poi...

In this article, we define a new space named the modular-like space with its related concepts to prove the existence of a fixed point and a point of coincidence for mappings on this space. Also, we defined Ćirić-Reich-Rus type weakly contractive mappings on modular-like spaces and discussed some conditions that guarantee the existence of the fixed...

In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where aĆirić type contraction was empl...

In this paper we define a new class of mappings called (θ, α +)− proximal admissible contrac-tionse and obtain a unique best proximity point for such mappings in the setting of complete generalized metric space. Our result is an extension of comparable results in the existing literature. Some examples are presented to support the results proved her...

In this article, we consider a wider class of nonexpansive mappings (locally related quasi-nonexpansive) than monotone nonexpansive mappings. We obtained the convergence of fixed point for quasi ϱ-preserving locally related quasi-nonexpansive mappings in hyperbolic space. An iterative process is also used to obtain the convergence results for this...

In this paper, we introduce two new classes of mappings known as λ-enriched strictly pseudocontractive mappings and ΦT-enriched Lipshitizian mappings in the setup of a real Banach space. In addition, a new modified mixed-type Ishikawa iteration scheme was constructed, and it was proved that our iteration method converges strongly to the common fixe...

In this paper, we introduce some new types of extended Geraghty contractions, called (α, β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point...

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the...

In this paper, we introduce the notion of ω-interpolativeĆirić-Reich-Rus-type proximal contraction. We obtain some best proximity point results for these mappings using the concept of ω-admissibility in complete metric spaces. Some best proximity results are extended to partial ordered metric spaces and graphical metric spaces. Several new definiti...

In this paper, we provide a short, comprehensive, and brief proof for Caristi-Kirk fixed point result for single and set-valued mappings in cone metric spaces. In addition, we partially addressed an open problem in which Caristi-Kirk fixed point result in cone metric spaces reduces to a classical result in metric spaces and provided a brief justifi...

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and prese...

This article presents the E -parametric metric space, which is a generalized concept of parametric metric space. After that, the discussion is concerned with the existence of fixed points of single and multivalued maps on E -parametric metric spaces satisfying some contractive inequalities defined by an auxiliary function.

Fixed-point theorems in metric spaces have extensively applied to a wide variety of mathematical problems, these kinds of results based upon some strong suppositions in metric spaces. In the current chapter, some weakly Kannan type generalized and weakly Kannan type proximal contractive mappings are introduced. Using these contractive conditions, w...

In this paper, we presented some new weaker conditions on the Proinov-type contractions which guarantees that a self-mapping T has a unique fixed point in terms of rational forms. Our main results improved the conclusions provided by Andreea Fulga (On (ψ, ϕ)−Rational Contractions) in which the continuity assumption can either be reduced to orbital...

In this paper, we discuss some (coincidence) best proximity point results for generalized proximal contractions and -proximal Geraghty contractions in controlled metric type spaces. To clarify our study, various examples are given and some conclusions are drawn. 1. Introduction and Preliminaries To solve the equation ( is a mapping defined on a su...

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx, Ty)) ≤ ϕ(d(x, y)), Proinov proved some fixedpoint theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierr...

This paper deals with a well known open problem raised by Kannan (Bull. Calcutta Math. Soc., 60: 71-76, 1968) and B. E. Rhoades (Contemp. Math., 72: 233-245, 1988) on the existence of general contractions which have fixed points, but do not force the continuity at the fixed point. We propose some new affirmative solutions to this question using two...

In this note, we define Meir-Keeler contraction in -metric spaces. Further, by adding the concept of -admissible mappings, we define generalized -Meir-Keeler contraction and used it for examining the existence and uniqueness of fixed points. Various results are also given as a consequence of our results. 1. Introduction and Preliminaries The Banac...

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional...

In this paper, firstly, we introduce some new generalizations of $F- contraction, F- Suzuki contraction, and F- expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value pro...

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler’s Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our pr...

Fixed points of monotone -nonexpansive and generalized -nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.

We introduce double and triple F -expanding mappings. We prove related fixed point theorems. Based on our obtained results, we also prove the existence of a solution for fractional type differential equations by using a weaker condition than the sufficient small Lipschitz constant studied by Mehmood and Ahmad (AIMS Math. 5:385–398, 2019) and Hanadi...

In this paper, we introduce the reversal of generalized Banach contraction principle and mean Lipschitzian mapping respectively. Secondly, we prove the existence and uniqueness of fixed points for these expanding type mappings. Further, we extend Wardowski’s idea ofF-contraction by introducing the reversed generalized F-contraction mapping and use...

In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b-metric space, fuzzy b-metric space, and extended fuzzy b-metric space. We use f , g, h, three noncomparable functions as follows: m q ðμ, η, t + s + wÞ ≥ m q ðμ, ν, t/f ðμ, νÞÞ * m q...

In this paper, we introduce generalized --fuzzy contractive mappings and generalized --fuzzy contractive mappings and prove existence of fixed point for such mappings. Our results generalize and improve the recent work of Gopal and Vetro (Iranian journal of fuzzy systems, 11 (2014), 95–107). Some equivalent conditions of our results are presented....

Metal-organic frameworks (MOF(n)) are organic-inorganic hybrid crystalline porous materials that consist of a regular array of positively charged metal ions surrounded by organic ‘linker’ molecules. The metal ions form nodes that bind the arms of the linkers together to form a repeating, cage-like structure. Moreover, in a chemical structure or mol...

This article contain the concepts of fuzzy (α-η) and fuzzy (β-ψ)-generalized proximal contractive mappings in the setup of b-fuzzy metric spaces. We proved the existence of coincidence and best proximity points of fuzzy (α-η)- and fuzzy (β-ψ)-generalized proximal contractions on b-fuzzy metric spaces. Some nontrivial examples are provided to elabor...

In this paper, we discuss about various generalizations of admissible mappings. Furthermore, we extend the concept of admissible to generalize rational Geraghty contraction in metric space. With this new contraction mapping, we establish some fixed-point theorems in metric space. The obtained result is verified with an example. 1. Introduction and...

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M ( x , y , t...

Citation: Aslam, M.S.; Bota, M.F.; Mohammad, S.R.C.; Guran, L.; Saleem, N. Common Fixed Points Technique for Existence of a Solution of Urysohn Type Integral Equations System in Complex Valued b-metric Spaces. Mathematics 2021, 9, 400. https://doi.org/10.3390/math9040400 Academic Editors: Simeon Reich and Temirkhan Aleroev

In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ciric type contraction was emp...

This paper is aimed at studying the uniqueness of coincidence best proximity point for ϑ,α+,g-proximal contractions in complete Branciari metric space. Throughout this article, discontinuity of the Branciari metric space is used and we obtained the desired results without assuming it as a continuous. Some examples are provided to validate the resul...

In this paper, we replied to an open problem related to a b−metric version of Banach's fixed point theorem. It was addressed with a partial answer by several authors, choosing a suitable contractive constant but we proved it in general, without adding any assumption in comparison with its classical one. Also, some new fixed point theorems for multi...

The aim of the paper was to prove some new fixed point theorems, coincidence point theorems and common fixed point theorems for multivalued F-contractions involving a binary relation that is not necessarily a partial order, in the context of generalized metric spaces (in the sense of Jleli and Samet). We also prove existence of common solutions to...

The aim of the paper is to prove some new fixed point theorems, coincidence point theorems and common fixed point theorems for multivalued F-contractions involving a binary relation that is not necessarily a partial order, in the context of generalized metric spaces (in the sense of Jleli and Samet). We also prove existence of common solutions to i...

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some α−Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing res...

In this paper we introduce the concepts of ψ -contraction and monotone ψ -contraction correspondence in “fuzzy b -metric spaces” and obtain fixed point results for these contractive mappings. The obtained results generalize some existing ones in fuzzy metric spaces and “fuzzy b -metric spaces”. Further we address an open problem in b -metric and “f...

In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - genera...

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some α−Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing res...

In this paper we introduce the concept of inverse C-class function in G-metric setting and established some fixed point theorems. We also put some examples in support of proved fixed point results.

The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (netw...

In this paper, we introduce the concept of coincidence best proximity point for multivalued Suzuki-type α-admissible mapping using θ-contraction in b-metric space. Some examples are presented here to understand the use of the main results and to support the results proved herein. The obtained results extend and generalize various existing results i...

In this paper, we prove the existence of optimal coincidence point and best proximity point in b-fuzzy metric space for two mappings satisfying certain contractive conditions and prove some proximal theorems which provide the existence of an optimal approximate solution to some operator equations which are not solvable. We also provide an applicati...

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some α−Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing res...

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained...

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, somevcoincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame...

In this paper, we generalized the results presented in the paper W. Long, S. Khaleghizadeh, P. Salimi, S. Radenović and S. Shukla, Some new fixed point results in partially ordered metric spaces via admissible mappings, Fixed Point Theory Appl. (2014), 2014:117, in the framework of partial metric spaces by using C−class function in ordered structur...