# Anita TomarPt.L.M.S. Campus Sridev Suman Uttarakhand University Rishikesh-249201, India · Mathematics

Anita Tomar

Ph.D.

Pt.L.M.S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, India

## About

105

Publications

21,465

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Introduction

Anita Tomar is an alumnus of H. P. U. Shimla and Gurukula Kangri Vishwavidyalaya, Haridwar(India). Her research interests focus on Fixed Point Theory and its Applications. Recently, she edited a book entitled "Fixed Point Theory & its Applications to Real World Problem", Nova Science Publishers, New York, USA (ISBN 978-1-53619-336-7) indexed in Scopus. She is the guest editor of the special issue on “Fixed-Point Techniques and Applications to Real World Problem” of the Journal of Function Space.

Additional affiliations

December 1998 - present

**Department of Higher Education Uttarakhand**

Position

- Professor

Description

- Teaching and Research

Education

December 1999 - May 2003

January 1985 - January 1986

## Publications

Publications (105)

The survival of a unique fixed point plays a central role in metric fixed point theory and has numerous applications in day-to-day life. However, if a self map has multiple fixed points, then looking at the geometry of the collection of fixed points is extremely appealing and natural. As a result, it is interesting to study the fixed figure problem...

We give a method to establish a fixed point via partial b-metric for multivalued mappings. Since the geometry of multivalued fixed points perform a significant role in numerous real-world problems and is fascinating and innovative, we introduce the notions of fixed circle and fixed disc to frame hypotheses to establish fixed circle/ disc theorems i...

This work aims to prove new results in an M v b - metric space for a noncontinuous single-valued self-map. As a result, we extend, generalize, and unify various fixed-point conclusions for a single-valued map and come up with examples to exhibit the theoretical conclusions. Further, we solve a mathematical model of the spread of specific infectious...

We are pleased to invite you and your colleagues to contribute your research work to an Edited Book entitled "Banach Contraction Principle: A Centurial Journey" to be published by Springer. We firmly believe that your contribution will enrich the academic and intellectual content of the book along with opening up new avenues of research in this fie...

Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed point and study their geometry in a partial metric space by introducing some novel contr...

We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with α-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.

In this manuscript, we explore stunning fractals as Julia and Mandelbrot sets of complex-valued cosine functions by establishing the escape radii via a four-step iteration scheme extended with s-convexity. We furnish some illustrations to determine the alteration in generated graphical images and study the consequences of underlying parameters on t...

We utilize Hardy-Rogers contraction and CJM−contraction in a C * −algebra valued partial metric space to create an environment to establish a fixed point.
Next, we present examples to elaborate on the novel space and validate our result. We conclude the paper by solving a boundary value problem and a matrix equation as applications of our main resu...

We introduce an $ \mathcal{M-} $class function in an $ \mathcal{S-} $metric space which is a viable, productive, and powerful technique for finding the existence of a fixed point and fixed circle. Our conclusions unify, improve, extend, and generalize numerous results to a widespread class of discontinuous maps. Next, we introduce notions of a fixe...

The aim of this research work is to demonstrate the survival of exactly one common fixed point for nonlinear contractions without assuming containment of range spaces of an involved pair of mappings, commutativity, and continuity (or any of their weaker forms). It is interesting to note that these findings involve different techniques of proof and...

In fixed point theory, interpolation is acknowledged in numerous areas of research, for instance, earth sciences, metallurgy, surface physics, and so on because of its prospective applications in the estimation of signal sensation analysis. As a result, it is interesting to investigate the fixed point and fixed circle (disc) utilizing interpolative...

We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and ηb−regularity in parametric Nb-metric spaces to determine a unique fixed point, a unique fixed circle, and a greatest fixed disc. Further, we investigate the geometry of non-unique fixed points of a self mapping and demonstrate by illustrative examples...

Here, we develop escape criteria for pc(z) = sin(zn)-az+c, a; c 2 C, n 2, exploiting four different iterations of fixed point theory to explore various Mandelbrot sets which are different than the classical Mandelbrot set. Our concern is to utilize the lesser number of iterations that are necessary to attain the fixed point of the transcendental
co...

Taking into account the fact that the contractive conditions carry out the magnificent role in establishing coinci- dence and common fixed points, we introduce generalized condition (B) for self maps in G−metric spaces and utilize it to establish a unique fixed point, a unique common fixed point, and a unique coincidence point. Conclusively, we dea...

We familiarize AM and SAMcontractions involving rational terms to prove a best proximant for discontinuous set-valued maps in partially ordered metric spaces. In the sequel, we demonstrate that completeness of space or subspace is not mandatory for the survival of a best proximant of set-valued maps. Obtained outcomes are uni cations, extensions,...

In this manuscript, we correct, improve, generalize, and enrich the comparable results already present in the literature. Further, we use the Jungck-Noor iteration equipped with s-convexity to prove the escape criteria of the polynomial zn+a1z2−a2z+ a3, where a1, a2 and a3 are complex numbers, for visualizing the stunning nonclassical mutants of ce...

In this research, we look at the Julia set patterns that are linked to the entire transcendental
function f (z) = ae^z^n+ bz + c, where a, b, c ∈C and n ≥ 2, using the Mann iterative scheme,
and discuss their dynamical behavior. The sophisticated orbit structure of this function, whose
Julia set encompasses the entire complex plane, is described us...

Fibonacci-Mann iteration scheme is a newly de ned iteration process which is introduced by Alfuraidan and Khamsi [Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 96 (2) (2017), 307- 316]. In this paper, utilizing the Fibonacci-Mann iteration process, we explore Julia and M...

We establish some escape criteria via Jungck Mann fixed point iteration system with s-convexity for complex-valued polynomials of higher orders. As a result, we point out errors in the corresponding existing criterion and develop a correct technique to obtain the escape criterion for analogous fixed point iterations equipped with s-convexity. Furth...

Inthispaper,wegeneratesomenon-classicalvariantsofJuliaandMandelbrotsets,utilizing the Jungck-Ishikawa fixed point iteration system equipped with s-convexity. We establish a novel escape criterion for complex polynomials of a higher degree of the form zn + az2 − bz + c, where a, b, and c are complex numbers and furnish some graphical illustrations o...

This document is a printed form of MSC2020, an MSC revision produced jointly by the editorial staffs of Mathematical Reviews (MR) and Zentralblatt fu ̈r Mathematik (zbMATH) in consultation with the mathematical community. The goals of this revision of the Mathematics Subject Classification (MSC) were set out in the announcement of it and call for c...

We introduce a relational generalized Meir-Keeler contraction and a relational generalized Meir-Keeler contraction with rational terms in non-complete relational b−metric like spaces to establish non-unique fixed point results for a discontinuous single valued map. Also, we provide an illustrative example to demonstrate that a relational generalize...

We introduce a novel distance structure called a b-interval metric space to generalize and extend metric interval space. Also, we demonstrate that the collection of open balls, which forms a basis of a b-interval metric space, generates a T 0-topology on it. Further, we define topological notions like an open ball, closed ball, b-convergence, b-Cau...

We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn ) + az + c, where a, c ∈ C, n ≥ 2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these f...

We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of...

We introduce C ́iri ́c type ZR-contraction to investigate the existence of a single fixed point under a binary relation. In the sequel, we demonstrate that a variety of contractions are obtained as consequences of our contraction. Also, we provide illustrative examples to demonstrate the significance of C ́iri ́c type ZR-contraction in the existenc...

This issue is now closed for submissions. More articles will be published in the near future. Description The origin of fixed-point theory lies in the strategy of progressive approximation utilized to demonstrate the existence of solutions of differential equations first presented in the 19th century. However, classical fixed-point theory was estab...

The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly mini-hedral cone, and scalar weighted cone assuming the cone to be strongly mini-hedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of t...

We demonstrate that the C−class functions, pair (h, f) upper-class functions, cone C−class functions, 1−1− up-class functions, multiplicative C−class functions, inverse−C−class functions, CF −simulation functions, C∗−class functions are powerful and fascinating weapons for the generalization, improve- ment, and extension of considerable conclusions...

The aim of this Special Issue is to collect original research and review articles related to the development of the fixed-point theory. We welcome submissions discussing methods of nonlinear analysis and the latest advancements for solving real-world problems using techniques associated with fixed point theory.

Compatibility of type (E) and weak subsequential continuity is utilized in a fuzzy metric space for the existence of a common fixed point. Illustrations and an application are stated to elucidate our outcomes.

In this note, with the help of examples, we point out that C∗−algebra-valued metric space is more general and results in this space are proper generalizations\extensions of the corresponding results in the literature in standard metric spaces. Hence
results of C∗−algebra-valued metric spaces do not coincide with (can not be
derived from) the result...

The common fixed point for ordered generalized φ−contraction in the environment of an ordered fuzzy metric space is determined under minimum possible conditions. A result in ordered metric space is also obtained. The work is supported with a suitable example. Further, as an application, the utility of the present work is shown by solving functional...

We introduce a notion of a fixed ellipse to study the geometric properties of the set of nonunique fixed points of a discontinuous self map and establish fixed ellipse theorems. Further, we verify these by illustrative examples with geometric interpretations to demonstrate the authenticity of the postulates. Paper is concluded by a discussion of ac...

We familiarize a notion of a fixed circle in a partial metric space which is not necessarily the same as a circle in a Euclidean space. Next, we establish novel fixed circle theorems and verify these by illustrative examples with geometric interpretation to demonstrate the authenticity of the postulates. Also, we study the geometric properties of t...

We introduce the notions of a generalized -contraction, a generalized -weak contraction, a -weak JS-contraction, an integral-type -weak contraction, and an integral-type -weak JS-contraction to establish the fixed point, fixed ellipse, and fixed elliptic disc theorems. Further, we verify these by illustrative examples with geometric interpretations...

In this manuscript, we initiate an almost α-F-contraction and an almost α-F-weak contraction in the setting of partial metric spaces and establish adequate conditions for the existence of fixed points. The obtained results generalize the classical and recent results of the literature, which are validated by suitable examples. As applications of the...

We familiarise with the concepts of contractiveness and expansiveness in a C∗−algebra valued partial metric space and create an environment for the existence of fixed point in it. We solve an integral equation and an operator type equation as an application of main result. Further we give some examples to elaborate C∗−algebra valued partial metric...

We demonstrate the presence of a single fixed point on M− metric spaces for generalized F (ψ, ϕ)-contractions using α−admissibility and C−class functions. Further, we provide an answer to an open problem regarding the existence and uniqueness of a fixed point of a classical Chatterjea contraction on an M−metric space, which is still open. Our obtai...

The book “Fixed Point Theory & its Applications to Real World Problems” is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further ex...

In 2014 was introduced C-class and pair upper Class functions that cover more papers before and after that .base on them some other ideas like :1-1-upclass functions,multiplicative C-class functions,inverse-C-class functions,CF-simulation functions were planed.In this glance we look for some condition that can use them or can not.

We familiarize notions of continuity, an interval circle, an interval disc, a near-fixed interval circle, a near-fixed interval disc, and their equivalence classes in a metric interval space to study the geometric properties of non-unique near-fixed points. Further, we establish near-fixed point, near-fixed interval circle, and near-fixed interval...

We investigate the geometry of the collection of non-unique fixed points in a b-metric space by introducing notions of a fixed ellipse and a fixed elliptic disc. We explore some new postulates which are necessary for the collection of non-unique fixed points to include an ellipse or an elliptic disc. Results so obtained, are validated by suitable i...

We introduce Mvb-metric to generalize and improve Mv-metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on Mvb-metric space and to create an environment for the survival of a unique fixe...

In this article, we prove coincidence point theorems for comparable ψ-contractive mappings in ordered non-Archimedean fuzzy metric spaces utilizing the recently established concept of T-comparability and relatively weaker order theoretic variants. With a view to show the usefulness and applicability of this work, we solve the system of ordered Fred...

We introduce relation theoretic contractions to establish a fixed point in F−metric spaces. Numerical examples are also given to illustrate the theoretical finding. As applications of our main result, we solve two point boundary value problems.

Book of Abstracts,
International e-Conference on Fixed Point Theory and its Applications to Real World Problems (FPTARWP2020) Satuarday, June 27, 2020 Organised by Prof. Anita Tomar,
Department of Mathematics, Government Post Graduate College Maldevta, Raipur Dehradun (Uttarakhand) India as Online Live Conference.
https://youtu.be/cqz4uUwy5lo

We first familiarise with δ-Hardy Roger type contraction in the frame work of metric space. Then, well-posedness, data dependence, existence and uniqueness results of strict fixed point for δ-Hardy Roger type contraction are presented. The obtained results generalize the existing results in the literature. Applications to an integral inclusion equa...

Some strict coincidence and common strict fixed point results are obtained ac- knowledging the notion of faint compatibility recently introduced by Tomar et al. (Coincidence and common strict fixed point of a faintly compatible hybrid pair of maps, Elect. J. Math. Anal. Appl., 5(2)2017, 298-305) via C-class functions that cover a large class of con...

We establish a relation theoretic version of the main result of Aydi et al. [H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric space, Topol. Appl. (159), 2012, 3234-3242] and extend the results of Alam and Imdad [A. Alam, M. Imdad, Relation-theoretic contraction priciple, J. Fixed Point Theory...

The aim of this article is to introduce the notion of almost α-Hardy-Rogers-F-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we...

Some coincidence and common fixed points are established in G-metric spaces via C-class functions covering an extensive class of contractive conditions. Our outcomes do not rely on the completeness of space/subspace, the continuity or the containment of range space of included tangential pair of single valued mappings. Some interesting examples are...

A-subsequential continuity, A-compatibility of type (E), compatibility of type (E) and weak subsequential continuity in a intuitionistic fuzzy metric space are introduced and the applicability of these notions in establishing the unique common fixed point is demonstrated. An example is given to outline our outcomes and the system of Fredholm equati...

In this paper, we prove two strict coincidence and strict common
fixed point theorems for weakly compatible hybrid pairs of strongly tangential mappings satisfying F-contraction, in a metric space. An example and an application to functional equations arising in dynamic programming is given to illustrate our results. In the sequel several known res...

Motivated by the fact that most of the times techniques used to establish coincidence and common fixed point do not require triangle inequality of the distance function, an attempt has been made in this paper to obtain coincidence and common fixed point theorems for S and T-compatible of type (E) and S and T- sub-sequentially continuous pairs of se...

The common fixed and the common stationary point in a symmetric space using Hausdorff distance and δ-distance respectively are established. Results obtained are utilised to solve the functional equations in dynamic programming and Volterra integral inclusion and are supported by illustrative examples.

A generalized condition (B) is introduced in the context of GP- metric spaces to establish coincidence and common fixed point of discontinuous mappings and utilized to solve the integral equation and the functional equation arising in dynamic programming. Our results are absolutely novel and provide a new dimension in fixed point theory and can not...

In this paper, we introduce new notion of common limit in the range property (CLRfg) for a pair of self map which is a proper generalization of common limit in the range property (CLRg) for a pair of self maps and discuss the existence of coincidence and common fixed point for weakly compatible self maps via property (E.A.) and its variants in intu...

The aim of this paper is to establish coincidence and common fixed point theorems for a discontinuous noncompatible pair of self-maps in noncom- plete metric space without containment requirement of range space of involved maps acknowledging the notion of F-contraction introduced by Wardowski [D. Wardowski, Fixed points of a new type of contractive...

The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space ac- knowledging the notion of Ku ̈nzi et al. [Ku ̈nzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M., O ̈ztu ̈rk A., Fixed point theorems on quasi-...

In this paper, we discuss strict coincidence and common strict fixed point of strongly tangential hybrid pairs of self-mappings satisfying Kannan type contraction via δ− distance, which is not even a metric. Also coincidence and common fixed point is established using Hausdorff metric. Consequently, several known results are extended, generalized a...

In this paper, we introduce the notion of subsequential continuity for a hybrid pair of maps and combine this concept with compatibility, to establish a coincidence and common fixed point theo- rem for a hybrid quadruple of maps. Our main result also demonstrates that several fixed point theorems can be unified using implicit relations. We also giv...

In this paper, we establish strict coincidence and strict common fixed point of strongly tangential hybrid quadruple satisfying C ́iric ́ type contraction via δ-distance, which is not even a metric. Also coincidence and common fixed point is established using Hausdorff metric. Consequently, several known results are extended, generalized and improv...

In this paper, we introduce conditional compatibility, faint com- patibility and conditional reciprocal continuity to a hybrid pair of maps in- volving a single-valued and a multivalued map using δ-distance and establish strict coincidence and common strict fixed point of a faintly compatible hy- brid pair without containment requirement of range s...

The paper is aimed to generalize and improve the results of Bisht and Shahzad [Faintly compatible mappings and common fixed points, fixed point theory and applications, 2013, 2013:156]. The significance of this paper lies in the fact that coincidence and common fixed point theorems under C ́iri ́c type contractive condition via faint compatibility...

Coincidence and common �fixed point of six self maps satisfying F-contractions are established via common limit in the range property without exploiting the notion of continuity or containment of range space of involved maps or completeness of space/subspace. Our results generalize, extend and improve the analogous recent results in literature.

The aim of this paper is to establish the existence of coincidence and common fixed point of F-contractions via CLRST property. Our results generalize, extend and improve the results of Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2012) 2012:94, 6 pages,...

The question of continuity of contractive map and in particular continuity at fixed points emerged with the publication of research papers by R. Kannan in 1968 and 1969 respectively.In fact continuity of a map is essential prerequisite for establish- ing fixed point. Probably the foremost common fixed point theorem without using the notion of conti...

In this paper, we prove some common fixed point theorems for quadruple of weakly compatible self maps in normed Boolean vector space using property (E.A) and its variants. Our results extend and unify various known results in literature.

The aim of this paper is to present a simple and unified approach for the existence of coincidence and common fixed point on symmetric spaces. Some illustrative examples is also furnished to demonstrate that our results are genuine improvement of many other known results existing in literature.

The aim of this paper is to extend and generalize the theory of fixed point to theory of intuitionistic fuzzy fixed point. We prove common fixed point theorems for R-weakly commuting maps employing common property (E.A) in intuitionistic fuzzy metric space via implicit relations which are viable, productive and powerful tool in finding the existenc...

The aim of this paper is to investigate the existence and uniqueness of coincidence and common fixed point for weakly compatible self maps via property (E.A) and its variants in Normed Boolean Vector Space. Our results extend and improve the results of S. Mishra et al. [Fixed point theorems for a class of maps in normed Boolean vector spaces, Fixed...

The purpose of this paper is to utilize the property (E.A.) and its variants to prove existence of coincidence and common fixed points for occasionally weakly compatible and weakly compatible maps in fuzzy metric space. Our results generalize, extend and improve several relevant common fixed point theorems from the literature. We also furnish an il...

Recently, Bisht and Shahzad [Faintly compatible map- pings and common fixed points, Fixed point theory and applica- tions,2013,2013:156] introduced the notion of faintly compatible maps and proved some new fixed point theorems under both contractive and noncon- tractive conditions which allowed the existence of a common fixed point or multiple fixe...

In this paper we prove coincidence and common fixed point theorems for two pairs of weakly compatible self maps in fuzzy metric space using a fuzzy analogue of the Meir-Keeler type contractive condition. Our results substantially extend, generalize, and improve a multitude of well known results of the form existing in the literature for metric as w...

The aim of this paper is to establish common fixed point theorems for single valued maps satisfying general contractive conditions of integral type using weak compatibility wherein the conditions of completeness of the underlying subspaces and containment of ranges amongst involved maps is not needed. Moreover, an example and an application are als...

In the present paper, we prove a common fixed point theorem for even number of occasionally weakly compatible mappings in Non-Archimedean Menger PM-space. Our result never requires the completeness of the underlying space (or subspaces), containment of the ranges amongst involved mappings and continuity of the mappings. Our result extends and gener...

n this paper we have drawn a comparative analysis among convergence of Picard, Mann and Ishikawa iteration for the complex space.

This paper explores the common fixed point theorems involving two pairs of weakly compatible mappings. Also the property (E.A) is proved under a new contractive condition which is independent of the previous known contractive definitions.

We present common fixed point theory for generalized weak contractive condition in symmetric spaces under strict contractions and obtain some results on Invariant Approximations.

The aim of this paper is to present common fixed point theorem in fuzzy metric spaces, for four self maps, satisfying implicit relations. The results of B.Singh and M.S.Chauhan[16] are generalized in this paper. Also, the application of fixed points is studied for the Product spaces.

## Questions

Questions (5)

The Science and Engineering Research Board (SERB) INDIA is delighted to announce the availability of National Post Doctoral Fellowships (NPDF). This opportunity is open to eligible candidates, particularly PhD students. I extend a warm welcome to interested researchers to pursue their Post Doctorate with me and encourage them to apply for the National Post Doctoral Fellowships.

If anyone interested , read-Mv b-metric space

Some nice new results may be obtained in the new space. It would be my pleasure to help if required.

**Invitation to Contribute to an Edited Book**

*A Complete Century of Banach Contraction Principle in Metric Fixed Point Theory*

As editors, we are pleased to invite you and your colleagues to contribute your research work to an Edited Book entitled

*A Complete Century of Banach Contraction Principle in Metric Fixed Point Theory***to be published by***. We hope that this book will be a milestone for many researchers of fixed point analysis and allied areas.***Nova Science Publishers**Please go through the details below for the deadlines.

**Full chapter submission:**July 19, 2023

**Review results:**Aug. 19, 2023

**Revision Submission:**Sept. 08, 2023

**Final acceptance/rejection notification:**Sept.23, 2023

**Submission of final chapters to Springer:**Sept.28, 2023

Email your papers to

*anitatmr@yahoo.com**or*