Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

The aim of this paper is to establish the existence and uniqueness of the common solution for the system of nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/fredholm-equation">Fredholm integral equations</a>, nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/volterra-integral-equation">Volterra integral equations</a> and nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/fractional-differential-equations">fractional differential equations</a> using the <a href="https://www.sciencedirect.com/topics/mathematics/common-fixed-point">common fixed point</a> results equipped with illustrative examples. Some common fixed point results satisfying the generalized contraction condition involving&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi is="true">w</mi></math>-distance and weak altering distance functions are proved. Then, an example is provided to support the usability of our result along with numerical experiments.

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Journal of Computational and Applied Mathematics

Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations

In this article, we prove some new common fixed point results under the generalized contraction condition using w-distance and weak altering distance functions. Also, the validity of the results is demonstrated by an example along with numerical experiment for approximating the common fixed point. Later, as applications, the unique common solutions for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations of Caputo type are derived.

Mathematica Slovaca

Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations

The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in b-metric spaces with supportive examples. We also approximate the common fixed point by Jungck-Picard and Picard iteration procedures along with the P property of the mappings. Further, (T,f)-stability of Jungck-Picard iterative and T-stability of Picard iterative schemes are proved. © 2022 World Scientific Publishing Company.

World University root node

Asian-European Journal of Mathematics

On existence and approximation of common fixed points in b -metric spaces

Journal of Advanced Mathematical Studies

Some common and coincidence fixed points of weakly compatible mappings in cone metric spaces

Advances in Fixed Point Theory

Approximating common fixed points under generalized Rational contractions in 2-banach spaces with applications

The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces. © 2019, Universitat Politecnica de Valencia. All rights reserved.

Fulltext

Applied General Topology

Approximation of common fixed points in 2-banach spaces with applications

In this paper, we introduce Prešić type mappings in ultrametric spaces and study the generalization of the Banach contraction principle by obtaining common fixed points for a pair of mappings in product spaces. Further, we investigate coincidence value and common fixed point of self mappings satisfying Prešić type contractive conditions in ultrametric spaces. Then we show how the common fixed point is approximated by various iteration schemes in ultrametric spaces. Also, stability of those iteration schemes is investigated. Examples are given to support our results. As an application, we obtain well-posedness of the common fixed point problem. © 2018, Springer International Publishing AG, part of Springer Nature.

Journal of Fixed Point Theory and Applications

Approximation and stability of common fixed points of Prešić type mappings in ultrametric spaces

In this paper, we define a generalized [Formula presented]-contraction and derive some new coupled fixed point theorems in cone metric spaces with total ordering condition. An illustrative example is provided to support our results. As an application, we utilize the results obtained to study the existence of common solution to a system of integral equations. We also present an application to Markov process. © 2018 Ivane Javakhishvili Tbilisi State University

Transactions of A. Razmadze Mathematical Institute

New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov process

In this paper, we generalize Nadler's result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler's type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces. © 2017 World Scientific Publishing Company.

On Nadler type results in ultrametric spaces with application to well-posedness

The aim of this paper to establish the existence and uniqueness of coincidence and common fixed points of Nadler type set-valued mappings under various generalized contractive conditions in the context of ultrametric spaces. Illustrative examples are provided to support our results. As an application, we have obtained well-posedness of the common fixed point problems. The presented results generalize several existing results in the literature in ultrametric space setting. © 2017, African Mathematical Union and Springer-Verlag Berlin Heidelberg.

Afrika Matematika

Generalized Nadler type results in ultrametric spaces with applications to well-posedness

In this paper, we introduce the concept of set-valued Prešić-Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping besides furnishing illustrative examples to highlight the realized improvements in the context of ultrametric spaces. Our results generalize and extend some known results in the literature. © 2017 World Scientific Publishing Company.

Set-valued contraction mappings of Prešić-Reich type in ultrametric spaces

In this paper, we study the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping satisfying generalized set-valued Prešić–Reich type contractive condition in ultrametric spaces without the property of completeness. As an application, the well-posedness of a common fixed point problem is proved. An example is given to illustrate our results. Our results generalize and extend the results of Prešić–Reich in the context of ultrametric spaces. © 2016, Springer International Publishing.