scholarly journals Nadler’s Theorem on Incomplete Modular Space

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1927
Author(s):  
Fatemeh Lael ◽  
Naeem Saleem ◽  
Liliana Guran ◽  
Monica Felicia Bota
Keyword(s):  
Fixed Point ◽  
Modular Space ◽  
Integral Inclusion ◽  
Modular Spaces

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler’s Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our proposed version of Nadler’s theorem.

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.

Amenability and Fixed Point Properties of Semitopological Semigroups in Modular Vector Spaces

2019 ◽  
Vol 63 (3) ◽  
pp. 692-704
Author(s):  
Khadime Salame
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Continuous Functions ◽  
Modular Space ◽  
Modular Spaces ◽  
Fixed Point Properties ◽  
Uniformly Continuous ◽  
Locally Convex

AbstractIn this paper, we initiate the study of fixed point properties of amenable or reversible semitopological semigroups in modular spaces. Takahashi’s fixed point theorem for amenable semigroups of nonexpansive mappings, and T. Mitchell’s fixed point theorem for reversible semigroups of nonexpansive mappings in Banach spaces are extended to the setting of modular spaces. Among other things, we also generalize another classical result due to Mitchell characterizing the left amenability property of the space of left uniformly continuous functions on semitopological semigroups by introducing the notion of a semi-modular space as a generalization of the concept of a locally convex space.

Nonlinear iterative algorithms for quasi contraction mapping in modular space

2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Robabe Moradi ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Double Sequence ◽  
Iterative Algorithms ◽  
Modular Space ◽  
Matlab Software ◽  
Numerical Examples ◽  
Modular Spaces

AbstractIn this paper, we introduce new nonlinear iterative algorithms. These algorithms are used to study the convergence of generated iterative sequences in modular spaces. Moreover, we introduce a new double sequence iteration and prove that sequences converge strongly to a fixed point of a ρ-quasi contraction mapping in modular spaces. Finally, some illustrative numerical examples (using the Matlab software) are presented.

A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

2021 ◽  
Vol 78 (1) ◽  
pp. 59-72
Author(s):  
Parbati Saha ◽  
Pratap Mondal ◽  
Binayak S. Chqudhury
Keyword(s):  
Fixed Point ◽  
Stability Problem ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Modular Space ◽  
Generalized Contraction ◽  
Mathematical Structures ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
Rassias Stability

Abstract In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

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.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

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.  

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

Stability Property of Functional Equations in Modular Spaces: A Fixed-Point Approach

2021 ◽  
Vol 109 (1-2) ◽  
pp. 262-269
Author(s):  
P. Saha ◽  
Pratap Mondal ◽  
B. S. Choudhury
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Stability Property ◽  
Fixed Point Approach ◽  
Modular Spaces
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