scholarly journals Applications of measure of noncompactness to coupled fixed points and systems of integral equations

2018 ◽  
Vol 19 (1) ◽  
pp. 537 ◽  
Author(s):  
A. Samadi
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Systems Of Integral Equations ◽  
Coupled Fixed Points

scholarly journals Coupled Optimal Results with an Application to Nonlinear Integral Equations

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 73
Author(s):  
Pulak Konar ◽  
Sumit Chandok ◽  
Shrutinil Dutta ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Nonlinear Integral Equations ◽  
Control Functions ◽  
Coupled Fixed Points

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.

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 Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

2021 ◽  
Vol 37 (3) ◽  
pp. 407-416
Author(s):  
SHAHRAM BANAEI ◽  
◽  
VAHID PARVANEH ◽  
MOHAMMAD MURSALEEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Fréchet Space ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Type Integral ◽  
Systems Of Integral Equations

"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."

scholarly journals Coupled fixed points and α-dense curves

2016 ◽  
Vol 32 (3) ◽  
pp. 323-330
Author(s):  
G. GARCIA ◽  
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonexpansive Mappings ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Compactness Condition ◽  
New Iterative Method ◽  
Coupled Fixed Points

We present a new iterative method, based on the so called α-dense curves, to approximate coupled fixed points of nonexpansive mappings. Compactness condition on the mapping or its domain of definition is necessary. As application, we construct a sequence which converges to a solution of certain system of integral equations of Volterra type.

scholarly journals The solvability of a class of system of nonlinear integral equations via measure of noncompactness

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5969-5991 ◽  
Author(s):  
Habibollah Nasiri ◽  
Jamal Roshan
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
General System ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Nonlinear Functional ◽  
Functional Integral Equations ◽  
Class Of Functions

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space. In this regard we present some theory and results on the existence of tripled fixed points and some basic Darbo?s type fixed points for a class of operators in Banach spaces. Also as an application we discuss the existence of solutions for a general system of nonlinear functional integral equations which satisfy in new certain conditions. Further we give an example to verify the effectiveness and applicability of our results.

scholarly journals Some Results on N-Tupled Coincidence and Fixed Points of Graphs on Metric Spaces and an Application to Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Ahmed H. Soliman ◽  
Tamer Nabil
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Systems Of Integral Equations ◽  
Theoretical Results

In this work, we establish some N-tupled common coincidence and N-tupled common fixed points for the mappings satisfying a (φ-ψ)-type contractive condition in a complete metric space endowed with a directed graph (for short digraph). Also, we apply our theoretical results to study the existence and uniqueness of solutions for systems of integral equations.

scholarly journals The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2130
Author(s):  
Hasanen A. Hammad ◽  
Amal A. Khalil
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Integral Equations ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
General Class Of Functions ◽  
Functional Integral Equations ◽  
Class Of Functions

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

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