scholarly journals C*-Algebra Valued Modular G-Metric Spaces with Applications in Fixed Point Theory

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2003
Author(s):  
Dipankar Das ◽  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra ◽  
Hamurabi Gamboa Rosales ◽  
Arvind Dhaka ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
C Algebra ◽  
Modular Metric Spaces ◽  
Class Function ◽  
New Type ◽  
The Stability

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.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

scholarly journals Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Choonkil Park ◽  
Manuel de la Sen ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
New Type ◽  
Uniqueness And Existence

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

scholarly journals On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Mi Zhou ◽  
Xiao-Lan Liu ◽  
Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Common Property ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
Contraction Condition ◽  
New Type ◽  
The One

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

scholarly journals Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 726-742
Author(s):  
Esad Jakupović ◽  
Hashem Masiha ◽  
Zoran Mitrović ◽  
Seyede Razavi ◽  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Point Theory ◽  
C Algebra ◽  
Coupled Fixed Points

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C*-algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.

scholarly journals Determination of the Some Results for Coupled Fixed Point Theory in C*-Algebra Valued Metric Spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 258-265
Author(s):  
Saleh Omran ◽  
Özen ÖZER
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Numerical Examples ◽  
C Algebra

In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spaces. We get a C*-algebra valued metric space which get values in noncomutative operators. We demonstrate existance and uniqeness of coupled fixed point in a such space. Besides, we support our results by giving numerical examples.

scholarly journals Fixed Point Theory For Generalized Quasi-contraction Maps In Modular Metric Spaces

2014 ◽  
Vol 10 (01) ◽  
pp. 54-60
Author(s):  
Hossein Rahimpoor ◽  
Ali Ebadian ◽  
Madjid Eshaghi Gordji ◽  
Ali Zohri
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Modular Metric Spaces ◽  
Contraction Maps

scholarly journals Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mappings ◽  
New Type ◽  
The Given ◽  
Kannan Contraction

In this paper, we use interpolation to obtain fixedpoint and common fixed point results for a new type of Kannan contraction mappings in complete metric and b -metric spaces. Our results extend and improve some results on fixed point theory in the literature. We also give some examples to illustrate the given results.

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