$$\mathcal {JHR}$$
                
                  
                    JHR
                  
                
              -operator pairs in 
                
                  
                
                $$C^{*}$$
                
                  
                    
                      C
                      
                        
                        ∗
                      
                    
                  
                
              -algebra-valued modular metric spaces and related fixed point results via 
                
                  
                
                $$C_{*}$$
                
                  
                    
                      C
                      
                        
                        ∗
                      
                    
                  
                
              -class functions

This article introduces a new type of C*-algebra valued modular G-metric spaces that is more general than both C*-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C*-algebra valued modular G-metric spaces are discussed using the “C*-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.

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

Canadian Mathematical Bulletin ◽

10.4153/cmb-2015-029-x ◽

2016 ◽

Vol 59 (01) ◽

pp. 3-12 ◽

Cited By ~ 2

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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Some fixed point theorems in modular metric spaces

The Journal of Nonlinear Sciences and Applications ◽

10.22436/jnsa.009.06.78 ◽

2016 ◽

Vol 09 (06) ◽

pp. 4381-4387 ◽

Cited By ~ 3

Author(s):

Afrah A. N. Abdou

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Modular Metric Spaces

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Non-Unique Fixed Point Theorems in Modular Metric Spaces

Symmetry ◽

10.3390/sym11040549 ◽

2019 ◽

Vol 11 (4) ◽

pp. 549

Author(s):

Sharafat Hussain

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Unique Fixed Point ◽

Periodic Points ◽

Modular Metric Spaces ◽

Modular Spaces

This paper is devoted to the study of Ćirić-type non-unique fixed point results in modular metric spaces. We obtain various theorems about a fixed point and periodic points for a self-map on modular spaces which are not necessarily continuous and satisfy certain contractive conditions. Our results extend the results of Ćirić, Pachpatte, and Achari in modular metric spaces.

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