scholarly journals Fixed Point Theorems for Noncyclic Monotone Relatively ρ-Nonexpansive Mappings in Modular Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Nour-eddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Modular Spaces

In this paper, we obtain some fixed point results for noncyclic monotone ρ-nonexpansive mappings in uniformly convex modular spaces and uniformly convex in every direction modular spaces. As an application, we prove the existence of the solution of an integral equation.

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 Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

2002 ◽  
Vol 31 (4) ◽  
pp. 251-257 ◽  
Author(s):  
Wei-Shih Du ◽  
Young-Ye Huang ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Nonexpansive Mappings ◽  
Finite Union ◽  
Uniformly Convex ◽  
Weakly Compact ◽  
Nonconvex Sets ◽  
Firmly Nonexpansive ◽  
Asymptotically Regular

It is shown that every asymptotically regular orλ-firmly nonexpansive mappingT:C→Chas a fixed point wheneverCis a finite union of nonempty weakly compact convex subsets of a Banach spaceXwhich is uniformly convex in every direction. Furthermore, if{T i}i∈Iis any compatible family of strongly nonexpansive self-mappings on such aCand the graphs ofT i,i∈I, have a nonempty intersection, thenT i,i∈I, have a common fixed point inC.

scholarly journals Convergence of Ishikawa iterates of generalized nonexpansive mappings

1997 ◽  
Vol 20 (3) ◽  
pp. 517-520 ◽  
Author(s):  
M. K. Ghosh ◽  
L. Debnath
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strictly Convex ◽  
Strictly Convex Banach Spaces

This paper is concerned with the convergence of Ishikawa iterates of generalized nonexpansive mappings in both uniformly convex and strictly convex Banach spaces. Several fixed point theorems are discussed.

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 Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
T. Domínguez Benavides ◽  
P. Lorenzo Ramírez
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Geometric Property ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniform Convexity ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Measures Of Noncompactness ◽  
Modular Spaces

AbstractThis paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular spaces.

scholarly journals Generalised Presic Type Operators in Modular Metric Space and an Application to Integral Equations of Caratheodory Type Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Fahad Sameer Alshammari ◽  
K. P. Reshma ◽  
Rajagopalan R. ◽  
Reny George
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Contractive Mappings ◽  
Modular Spaces ◽  
Type Integral ◽  
Fixed Point Equation ◽  
Point Equation

Extending the Presic type operators to modular spaces, we introduce generalised Presic type w -contractive mappings and strongly w -contractive mappings in a modular metric space and establish fixed-point theorems for such contractions in modular spaces. Ulam–Hyers stability of the fixed-point equation involving Presic type operators is also discussed. Our results extend and generalise some known results in the literature. The results are supported by appropriate example and an application to Caratheodory type integral equation.

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

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