Convexity property and fixed-point theorems in CΩ-modular space

2021 ◽  
pp. 1-4
Author(s):  
Sarem H. Hadi ◽  
Zainab S. Madhi ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Study Finding ◽  
Modular Space ◽  
Convexity Property

The purpose of this study is to introduce a new concept of the modular space, which is CΩ-modular space, and then some of the convex properties are discussed. We also study finding fixed-point in CΩ-modular space.

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 Two Fixed-Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam Beygmohammadi ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Contractive Condition ◽  
Integral Type

First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type. Then we generalize fixed-point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974).

scholarly journals Fixed Point Theorems for a New Class of Mappings in Modular Spaces Endowed with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Nour-eddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Modular Space ◽  
New Class ◽  
Modular Spaces

In this paper, we discuss a class of mappings more general than ρ-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.

scholarly journals Expansive Mappings and Their Applications in Modular Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
A. Azizi ◽  
R. Moradi ◽  
A. Razani
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Nonlinear Integral Equations ◽  
Modular Spaces

Some fixed point theorems forρ-expansive mappings in modular spaces are presented. As an application, two nonlinear integral equations are considered and the existence of their solutions is proved.

scholarly journals Common fixed point theorems for several multivalued mappings on proximinal sets in regular modular space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
N. Faried ◽  
H. Abd El-Ghaffar ◽  
S. Hamdy
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Multivalued Mappings ◽  
Modular Metric Space ◽  
Proximinal Sets ◽  
Common Fixed Point Theorems

AbstractIn this paper, we found a common fixed point for several multivalued mappings on proximinal sets in regular modular metric space. Also, we introduced the notions of conjoint F-proximinal contraction as well as conjoint F-proximinal contraction of Hardy–Rogers-type for several multivalued mappings. Furthermore, we enhanced our results by giving an application in integral equations.

scholarly journals Some fixed point theorems for Kannan mapping in the modular spaces

2015 ◽  
Vol 37 ◽  
pp. 462 ◽  
Author(s):  
S. J. Hosseini Ghoncheh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Fatou Property ◽  
Modular Spaces ◽  
Kannan Mapping

In this article, a new version of Kannan mapping theorem in modular space is presented. The main result of this paper is the existence of fixed point of Kannan mapping in complete modular spaces that have Fatou property.

scholarly journals New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Weng-Seng Heng ◽  
Wei-Shih Du ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Convexity Property ◽  
Linear Spaces ◽  
Compact Metric Spaces

We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

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