scholarly journals Fixed point theorems for generalized asymptotic pointwise ρ-contraction mappings involving orbits in modular function spaces

2012 ◽  
Vol 25 (10) ◽  
pp. 1285-1290 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Modular Function ◽  
Function Spaces ◽  
Contraction Mappings ◽  
Modular Function Spaces

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 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.

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 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 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 Some KKM theorems in modular function spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1307-1313
Author(s):  
Nasrin Karamikabir ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Modular Function ◽  
Function Spaces ◽  
Minimax Inequality ◽  
Approximation Theorems ◽  
Coincidence Theorem ◽  
Modular Function Spaces ◽  
Ky Fan

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

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