Satish Shukla

Shri Vaishanav Institute of Technology & Science | SVITS · Department of Applied Mathematics

This paper introduces the notion of k-fuzzy metric spaces, which generalizes and extends the concept of fuzzy metric spaces due to George and Veeramani in [A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.] for the fuzzy sets involving more than one (k) parameters. It is shown that the to...

In this paper, we consider Caristi type mappings in the setting of 1-M-complete fuzzy metric-like spaces. We establish some fixed point theorems for such mappings and prove the fuzzy metric-like versions of Caristi theorem, Ekeland’s variational principle and Takahashi’s maximization theorem. Further, we show that these three types of results are e...

In 2017, Parvaneh et al. (J Math Anal 8(1):183–201, 2017) further extended rectangular metric space by introduced partial rectangular b-metric space and utilized the same to prove some fixed point results. Almost at the same time, Roshan et al. (Nonlinear Anal Model Control 21(5):614–634, 2016) generalized Geraghty fixed point results by proving so...

In this paper, we discuss some topological properties of graphical metric spaces and introduce the G -set metric with respect to a graphical metric. Some fixed point results are introduced which generalize the famous Nadler’s fixed point theorem.

In this work, we introduce the notion of relation-theoretic í µí¼‘-contractive mappings in cone metric spaces over Banach algebra which is equipped with a binary relation. Some fixed point results for such mappings are proved. Some examples are provided which illustrate the notions introduced and the results proved herein.

The purpose of this paper is to prove some Preši´Preši´c-Boyd-Wong type fixed point theorems in ordered metric spaces. The results of this paper generalize the famous results of Preši´Preši´c and Boyd-Wong in ordered metric spaces. We also initiate the homotopy result in product spaces. Some examples are provided which illustrate the results proved...

In this paper, some fixed point results for relation theoretic weak \(\varphi \)-contractions on cone metric spaces which is defined over a Banach algebra and equipped with a binary relation are proved. These results extend and generalize several results of metric and cone metric spaces. Some examples are provided which demonstrate the results prov...

In this article, we go on to discuss various proper extensions of Kannan’s two different fixed point theorems, and introduce the new concept of σc-function, which is independent of the three notions of simulation function, manageable functions, and R-functions. These results are analogous to some well-known theorems, and extend several known results...

The purpose of this paper is to introduce the notion of set-valued (𝛼, 𝑝)- weak contractions in cone metric spaces over Banach algebra and to prove some fixed point theorems for such mappings. The fixed point results of this paper generalize and extend several known fixed point results on cone metric spaces. An example in support of our results is...

In this work, we introduce the class of ordered weak ϕ-contractions in cone metric spaces over Banach algebras and prove some fixed point results for the mappings belonging to this new class. Our results generalize and extend some known fixed point results in cone metric spaces to the spaces equipped with a partial order. Some examples are given wh...

The purpose of this paper is to introduce a new type of operators in graphical metric spaces and to prove some fixed point results for these operators. Several known results are generalized and extended in this new setting of graphical metric spaces. The results are illustrated and justified with examples.

In the proof of Theorem 3.2 of our paper [1] it has been assumed that cin =a2n for all n 2 N, i = 1; 2; : : : ; k, where cin is an interior point of the cone P such that �(cin) < 1 for all n 2 N, i = 1; 2; : : : ; k and a 2 P is the contractive vector of the mapping T. We point out that, in general, the assumption \cin = a2n" is not valid since cin...

In this paper, we establish a relation-theoretic version of a famous fixed point result of Nadler on complete metric spaces endowed with a binary relation. Our results extend and generalize the recent result of A. Alam and M. Imdad (see [1], Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17(4) (2015), 693-702) and several oth...

The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove some fixed point results of contractive mappings on complex valued fuzzy metric spaces. Some examples are presented to support the results proved herein. Our results extend various results in the existing literature.

In this paper, we introduce the notion of weakly connected pair of mappings and prove some fixed point and common fixed point theorems for a pair of weakly connected mappings on cone metric spaces over Banach algebras which is endowed with a graph. Our results generalize the result of Altun et al. [9] in cone metric spaces over Banach algebra.

The main aim of this work is to unify di�erent classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy Z-contractive mappings. For this new class of mappings, suitable conditions are framed to ensure the existence of �xed point in M-complete fuzzy metric spaces (in the sense of George and Veeraman...

The main aim of this work is to unify different classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy Z-contractive mappings. For this new class of mappings, suitable conditions are framed to ensure the existence of fixed point in M-complete fuzzy metric spaces (in the sense of George and Veeram...

In this paper, we introduce the notions of α-ψφ-contractive and cyclic α-ψφ-contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces. The results presented here substantially generalize and extend several comparable results in the existing literature, in particular those of Kar...

In this paper, a common fixed point theorem for four mappings in cone metric spaces over Banach algebras is proved without assuming the normality of underlying cone. The results of this paper unify, generalize and extend some known results in cone metric spaces over Banach algebras. An example is presented which shows the significance of the result...

In this paper, we prove Boyd-Wong and Meir-Keeler type theorems in the frame of generalized metric spaces of Branciari type, without using Hausdorff assumption. Our results improve and generalize several well known results existing in the literature. In particular, we improve a recent result obtained by Jleli et al. in [M. Jleli, E. Karapınar, B. S...

In this article, we go on to discuss various proper extensions of Kannan’s two different fixed point theorems, and introduce the new concept of σc function, which is independent of the three notions of simulation function, manageable functions, and R-functions. These results are analogous to some well-known theorems, and extend several known result...

We prove some common fixed point results for two α-dominated mappings satisfying some restricted contractive conditions on a closed ball of a left (right) K-sequentially complete dislocated quasi metric space. Some examples are given to show the utility of our work. The results of this paper complement, extend and enrich several recent results in t...

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued �-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed poi...

In this paper, some fixed point theorems in a partial 𝑏-metric space endowed with a partial order are proved. The results of this paper generalize and extend the Banach contraction principle and some other known results in partial 𝑏-metric spaces endowed with a partial order. Some examples are given which illustrate the cases when new results can b...

We propose a new notion of multi-valued almost (GF; δ

In this paper, we introduce the generalized Kannan type �-admissible mappings in the setting of cone metric spaces equipped with Banach algebra. Our results generalize and extend the fixed point result for Kannan type mappings in metric and cone metric spaces. An example is presented which illustrates our main result.

In this paper, we introduce the notion of G-contractions on cone b-metric spaces over Banach algebras endowed with a graph G. Fixed point theorems for G-contractions are proved. Some examples are also provided to illustrate the main results presented in this paper, which extend and generalize several known results in cone b-metric spaces over Banac...

In this paper, we introduce the concept of linear cone 2- normed spaces and prove some fixed point results for generalized 7Z- Lipschitz contractions in linear cone 2-normed spaces endowed with a binary relation 71. We observe that the fixed point of the considered mappings can be approximated with Mann iteration scheme. Our results generalize and...

In this paper, the notion of G-(F, τ)-contractions in the context of partial rectangular metric spaces endowed with a graph is introduced. Some fixed point theorems for G-(F, τ)-contractions are also proved. The results of this paper generalize, extend, and unify some known results. Some examples are provided to illustrate the results proved herein...

In this paper, we introduce a new class of operators called fuzzy-Prešić-Ćirić operators. For this type of operators, the existence and uniqueness of fixed point in M-complete fuzzy metric spaces endowed with H-type t-norms are established. The results proved here generalize and extend some comparable results in the existing literature. An example...

In this short note, we show that every multiplicative metric on a nonempty set $X$ induces a metric on $X$ in such a way that the topologies induced by multiplicative metric and the induced metric are same. Therefore, the multiplicative metric spaces are a particular case of metric spaces. Further, the fixed point results for various multiplicative...

In this paper, we introduce the notion of α-admissible mappings in the setting of cone 2-metric spaces over Banach algebras. Some existence and uniqueness results of the fixed point of an α-φ-contractive mapping in cone 2-metric spaces are proved. Some examples are provided which illustrate the results proved herein.

Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with...

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a m...

In this paper, we define the cyclic-Prešić–Ćirić operators in metric-like spaces and prove some fixed point results for such operators. Our results generalize that of S.B. Prešić [Sur une classe d'inéquations aux différences finite et sur la convergence de certaines suites, Publications de l'Institut Mathématique (N.S.), 5(19):75–78, 1965] and seve...

In this paper, we introduce α-admissible mappings on product spaces and obtain fixed point results for α-admissible Prešić type operators. Our results extend, unify and generalize some known results of the literature. We also provide examples, which illustrate the results proved herein and show that how the new results are different from the existi...

In this work, we introduce the notion of relation-theoretic contractions in cone metric spaces with Banach algebra and prove some fixed point results for such contractions. Our results generalize and unify several known results in the setting of cone metric spaces with Banach algebra. An example is provided which illustrate the results proved herei...

In this paper, we establish some common fixed point theorems for two mappings satisfying set-valued Prešić-Chatterjea type contractive conditions. The new theorems generalize and unify some well-known theorems of the literature. We also provide some examples to illustrate and confirm the usability of the obtained results.

In this paper, we introduce the notions of ordered $F$-$(\mathcal{F},h)$% -contraction and subcontraction in the setting of partial metric spaces. Some fixed point theorems for ordered $F$-$(\mathcal{F},h)$-contraction and subcontraction in 0-$f$-orbitally complete partial metric spaces are proved. Our results generalize some recent results of metr...

In this paper, we define the Cyclic-Pre\v{s}i\'{c}-\'{C}iri\'{c} operators in metric-like spaces and prove some fixed point results for such operators. Our results generalize the results Pre\v{s}i\'{c} \cite{Pre1}, Pre\v{s}i\'{c} and \'{C}iri\'{c} \cite{Cir}, Shukla and Fisher \cite{Shu3}, Shukla and Abbas \cite{shukla} and several other known resu...

In this paper, we prove some common fixed point theorems for the mappings satisfying Prešić type contractive conditions in metric spaces. Our results generalize and extend the result of Prešić for some new type of contractive conditions. The common fixed point of mappings is approximated by a k-step iterative sequence. Some examples are provided to...

The purpose of this paper is to prove some fixed point theorems for set-valued mappings satisfying Pre\v{s}i\'{c}-Reich type contractive condition in cone metric spaces, without assuming the normality of cone. Our results generalize some known results in metric and cone metric spaces.

In this paper, we introduce the $\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.

Motivated by the recent work of Liu and Xu, we prove a generalized Banach fixed point theorem for the setting of cone rectangular Banach algebra valued metric spaces without assuming the normality of the underlying cone. Our work generalizes some recent results into cone rectangular Banach algebra valued metric spaces. An example to illustrate the...

In this paper, we compare relation between n-tuple fixed point results and fixed point theorems in abstract metric spaces and metric-like spaces. Actually, we show that the results of n-tuple fixed point can be obtained from fixed point theorems and conversely. Thus, some recent results about both fixed points and n-tuple fixed points are equivalen...

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan’s fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

Let (X, d) be a metric space and T : X → X be a mapping. In this work, we introduce the mapping ζ : [0, ∞) × [0, ∞) → R, called the simulation function and the notion of Z-contraction with respect to ζ which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx, Ty) and d(x, y)....

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In this paper, we introduce the weakly monotone Prešić type mappings in product spaces when the underlying space is an ordered cone metric space. Some fixed point results for such mappings are also proved which generalize and unify several known results in metric and cone metric spaces with normal cone. The results are supported by examples.

The purpose of this paper is to prove some fixed point theorems for fuzzy cyclic contractions without monotone property in O-complete fuzzy metric spaces. Our results extend the result of Gregori and Sapena \cite{Gre} for fuzzy cyclic contractions without monotone property in O-complete fuzzy metric spaces. Illustrative examples in support of new r...

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

The purpose of this paper is to establish some stability results for set-valued mappings satisfying Prešić type contraction condition in metric spaces. Also we generalize the Assad and Kirk's fixed point theorem for non-self mappings in product spaces, by proving a fixed point result for non-self set-valued mappings satisfying Prešić type contracti...

In this paper, the well known concept of cyclic contraction is generalized in product spaces by introducing a new class of operators called cyclic-Presic operators. A fixed point result for such operators is proved. Some examples are given to validate the results proved herein.

In this paper, we introduce the generalized Nadler G-contractions in cone metric spaces endowed with a graph and defined over a Banach algebra. A fixed point result for such mappings is proved. Our result generalizes some known results in metric and cone metric spaces. An example is presented which verifies the significance and usability of the res...

In this paper, the concept of fuzzy metric-like spaces is introduced which generalizes the notion of fuzzy metric spaces given by George and Veeramani [8]. Some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. These results generalize several comparable results from the current literature. We also provide...

The purpose of this paper is to establish some coincidence and common fixed point theorems for a set-valued and a single-valued mapping satisfying Prešić–Reich type contraction conditions in metric spaces. Our results generalize and extend some known results in metric spaces. An example is included which illustrate the results.

The purpose of this paper is to prove some fixed point theorems in ordered metric spaces with two comparable metrics. Our results generalize and unify the fixed point theorems of Pre\v{s}i\'{c}, Maia and some recent results from ordered metric spaces, into product spaces when underlying space is ordered. An iterative method for constructing the fix...

The purpose of this paper is to prove some Pre\v{s}i\'{c}-Boyd-Wong type fixed point theorems in ordered metric spaces. Also a homotopy result in product spaces is proved. To demonstrate the results examples are given.

The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.

The purpose of this paper is to discuss the existence of fixed points for new classes of mappings defined on an ordered metric space. The obtained results generalize and improve some fixed point results in the literature. Some examples show the usefulness of our results. MSC: 46N40, 47H10, 54H25, 46T99.

In this paper, we consider the set-valued contractions defined on product spaces when the underlying space is a complete metric space endowed with a graph. Some fixed point results for the so-called set-valued G-Prešić operators are established. Our theorems extend and generalize some known results in product spaces of the recent literature. As an...

In this paper we introduce set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces and prove the corresponding theorem of fixed point. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by Aydi et al....

We prove some fixed point theorems for ordered F-generalized contractions in ordered 0-f-orbitally complete partial metric spaces. Our results generalize some well-known results in the literature, in particular the recent result of D. Wardowski [Fixed Point Theory Appl. 2012, Article ID 94, 6 p. (2012; Zbl 06216206)] from metric spaces to ordered 0...

In this paper, we prove some fixed-point theorems for Reich-type contractions on cone rectangular metric spaces endowed with a graph without assuming the normality of cone. The results of this paper extend and generalize several known results from metric, rectangular metric, cone metric and cone rectangular metric spaces in cone rectangular metric...

The purpose of this paper is to prove some fixed point theorems in ordered metric spaces with two comparable metrics. Our results generalize and unify the fixed point theorems of Presic, Maia and some recent results from ordered metric spaces, into product spaces when underlying space is ordered. An iterative method for constructing the fixed point...

In this paper, we consider some fuzzy cyclic contractions and prove the existence and uniqueness of fixed points of operators belong to a class consisting fuzzy cyclic operators defined on a subset of a fuzzy metric space. We also furnish some illustrative examples to support our main results.

The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illust...

The purpose of this paper is to prove some coincidence and common fixed point theorems for a single-valued and a set-valued mapping satisfying Prešić type contractive conditions in metric spaces. Our results generalize and extend some known results.

In this paper, we introduce the generalized cyclic contractions on θ-complete partial cone metric spaces and prove a fixed point result in such spaces without assuming the normality of cone. Our result generalizes some known re-sults from metric and cone metric spaces in θ-complete cone metric spaces. For illustration examples are provided.

The purpose of this paper is to introduce the set-valued Prešić-Ćirić type contraction in 0-complete partial metric spaces and to prove some coincidence and common fixed point theorems for such mappings in product spaces, in partial metric case. Results of this paper extend, generalize and unify several known results in metric and partial metric sp...

In this paper, we generalize the Banach contraction principle by proving common fixed point theorems for mappings satisfying Prešić type conditions in 2-Banach spaces. The common fixed point is approximated by the k-Picard type and k-Mann type iteration schemes in product spaces. The results in this paper extend the results of Prešić in the framewo...

The purpose of this paper is to prove some coincidence and common fixed point theorems for ordered Prešić-Reich type contractions in ordered metric spaces. Results of this paper generalize and extend several known results from metric spaces into product spaces when the underlying space is an ordered metric space. An example illustrates the case whe...

The purpose of this paper is to prove some coincidence and common fixed point results for mappings satisfying Prešić type contraction condition in 0-complete ordered partial metric spaces. The results proved in this paper generalize and extend the results of Prešić and Matthews in 0-complete ordered partial metric spaces. Some examples are included...

In this paper, we prove some fixed point theorems for ordered Reich type contraction in cone rectangular metric spaces without assuming the normality of cone. Our results generalize and extend some recent results in cone rectangular metric spaces, cone metric spaces and rectangular metric space. Some examples illustrating the results are included.

In this paper, we introduce the notion of 0-σ-complete metric-like space and prove some common fixed point theorems in such spaces. Our results unify and generalize several well-known results in the literature and the recent result of Amini-Harandi [Fixed Point Theory Appl. 2012:204, 2012]. Some examples are included which show that the generalizat...

In this paper we introduce the concept of tvs-cone b-metric space over solid cone. Our results improve, generalize, extend, unify, enrich and complement recent fixed point results established by H. Huang and S. Xu, M. P. Stanic et al., A. S. Cvetkovic et. al. and M. H. Shah et al. The examples are given to illustrate the usability of our results.

In this paper, we introduce the notion of θ-Cauchy sequence and θ-complete-ness in the setting of partial cone metric spaces. Also, we consider Hardy-Rogers type mappings on partial cone metric spaces and prove some fixed point results without as-suming the normality of cone.

The purpose of this paper is to obtain the fixed point results for F-type contractions which satisfies a weaker condition than the monotonicity of self-mapping of a partially ordered metric-like space. A fixed point result for F-expansive mapping is also proved. Therefore, several well known results are generalized. Some examples are included which...

In this paper we extend some coupled coincidence and common fixed point theorems for a hybrid pair of mappings obtained by Abbas et al. (Fixed Point Theory Appl. 2012:4, 2012, doi:10.1186/1687-1812-2012-4) from the complete metric space to 0-complete partial metric spaces. An example showing that this extension is proper is given. MSC: 47H10, 54H...

The purpose of this paper is to introduce the notion of a fuzzy ℋ-weak contraction and prove a fixed point theorem for fuzzy ℋ-weak contractions without exploiting the notion of continuity in M-complete fuzzy metric spaces. Examples are given to show that our result is a proper extension of some known results in the literature.

We generalize the result of Prešić in metric-like spaces by proving some common fixed point theorems for Prešić type mappings in metric-like spaces. An example is given which shows that the generalization is proper.

We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.

We introduce some generalizations of Prešić type contractions and establish some fixed point theorems for mappings satisfying Prešić-Hardy-Rogers type contractive conditions in metric spaces. Our results generalize and extend several known results in metric spaces. Some examples are included which illustrate the cases when new results can be applie...

The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are al...