scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

scholarly journals Some Fixed Point Theorems in Modular Function Spaces Endowed with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Jaauad Jeddi ◽  
Mustapha Kabil ◽  
Samih Lazaiz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Function Spaces ◽  
Compact Sets ◽  
Modular Function Spaces

The aim of this paper is to give fixed point theorems for G-monotone ρ-nonexpansive mappings over ρ-compact or ρ-a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work.

scholarly journals Iterative Approximation of Fixed Point of Multivalued ρ-Quasi-Nonexpansive Mappings in Modular Function Spaces with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Sheila Amina Bishop ◽  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Point Theory ◽  
Function Spaces ◽  
Initial Value ◽  
Iterative Approximation ◽  
Modular Function Spaces ◽  
Nonlinear Mappings

Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in modular function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in modular function spaces. We prove some interesting theorems for ρ-quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem.

scholarly journals Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 130
Author(s):  
Mohamed Amine Farid ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Weak Topology ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Operator ◽  
Banach Algebras ◽  
Measure Of Weak Noncompactness

In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.

scholarly journals Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1253-1264 ◽  
Author(s):  
Hüseyin Işik ◽  
Duran Türkoğlu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Nonlinear Problems ◽  
Monotone Mappings ◽  
Mixed Monotone Property

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

THE EXISTENCE OF A SOLUTION OF THE NONLINEAR INTEGRAL EQUATION VIA THE FIXED POINT APPROACH

2021 ◽  
Vol 10 (7) ◽  
pp. 2977-2998
Author(s):  
T.A. Adeyemi ◽  
F. Akusah ◽  
A.A. Mebawondu ◽  
M.O. Adewole ◽  
O.K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Nonlinear Integral Equation ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Existence Of A Solution ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework of uniformly convex hyperbolic space and also propose a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex hyperbolic spaces. Furthermore, we establish some basic properties and some strong and $\triangle$-convergence theorems for these mappings in uniformly convex hyperbolic spaces. Finally, we present an application to the nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper extends and generalizes corresponding results in uniformly convex Banach spaces, CAT(0) spaces and other related results in literature.

scholarly journals Fixed Point Theorems of Binary Contraction Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhan Liu ◽  
Chuanxi Zhu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Large Class ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Problems ◽  
Existence Of Solution ◽  
Partially Ordered ◽  
Ordered Banach Spaces

The aim of this paper is to present the concept of binary comparable operators in partially ordered Banach spaces and prove several fixed point theorems under some contractive conditions. The results of this paper can be used to investigate a large class of nonlinear problems. As an application, we study the existence of solution of a nonlinear integral equation.

ON MODULATED TOPOLOGICAL VECTOR SPACES AND APPLICATIONS

2019 ◽  
Vol 101 (2) ◽  
pp. 325-332 ◽  
Author(s):  
WOJCIECH M. KOZLOWSKI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Modular Function ◽  
Function Spaces ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Modular Function Spaces ◽  
Bare Minimum ◽  
Minimalist Framework

We introduce a notion of modulated topological vector spaces, that generalises, among others, Banach and modular function spaces. As applications, we prove some results which extend Kirk’s and Browder’s fixed point theorems. The theory of modulated topological vector spaces provides a very minimalist framework, where powerful fixed point theorems are valid under a bare minimum of assumptions.

scholarly journals Convergence Results for Total Asymptotically Nonexpansive Monotone Mappings in Modular Function Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Maliha Rashid ◽  
Amna Kalsoom ◽  
Shao-Wen Yao ◽  
Abdul Ghaffar ◽  
Mustafa Inc
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Monotone Mappings ◽  
Modular Function Space ◽  
Convergence Results ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Extensive Class ◽  
Modular Function Spaces

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.

scholarly journals Common Fixed-Point Theorems in Modular Function Spaces Endowed with Reflexive Digraph

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jaauad Jeddi ◽  
Mustapha Kabil ◽  
Samih Lazaiz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Modular Function ◽  
Function Spaces ◽  
Modular Function Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

The purpose of this work is to extend the Knaster–Tarski fixed-point theorem to the wider field of reflexive digraph. We give also a DeMarr-type common fixed-point theorem in this context. We then explore some interesting applications of the obtained results in modular function spaces.

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