scholarly journals Sufficient conditions to solve two systems of integral equations via fixed point results

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Giuseppe Marino ◽  
Badriah A. S. Alamri ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Sufficient Conditions ◽  
Two Systems ◽  
Systems Of Integral Equations

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 Multi-valued fixed point theorem via F- contraction of Nadler type and application to functional and integral equations

2021 ◽  
Vol 39 (4) ◽  
pp. 83-95 ◽  
Author(s):  
Muhammad Shoaib ◽  
Muhammad Sarwar ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Sufficient Conditions

In this work, using F-contraction of Nadler type, common multi-valued fixed point results in the setting of b-metric space are established. With the assistance of the determined results sufficient conditions for the existence of common solutions to the systems of functional and integral equations are studied.

scholarly journals Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2763-2784
Author(s):  
Józef Banaś ◽  
Bilel Krichen ◽  
Bilel Mefteh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Lipschitz Continuity ◽  
Banach Algebras ◽  
Nonlinear Integral Equations ◽  
Systems Of Integral Equations ◽  
Sequential Continuity ◽  
Measures Of Weak Noncompactness

The paper is devoted to prove a few fixed point theorems for operators acting in WC-Banach algebras and satisfying some conditions expressed in terms of a generalized Lipschitz continuity and measures of weak noncompactness. Moreover, the assumptions imposed on the mentioned operators are formulated with help of weak topology and weak sequential continuity. Our fixed point results will be illustrated by proving the existence of solutions of an infinite system of nonlinear integral equations.

scholarly journals Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

2020 ◽  
Vol 53 (1) ◽  
pp. 236-248
Author(s):  
Tamer Nabil
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Nuclear Physics ◽  
Mixed Type ◽  
Coupled System ◽  
Existence Of A Solution ◽  
System Of Integral Equations ◽  
Nonlinear Coupled System ◽  
Systems Of Integral Equations ◽  
Quadratic Integral

AbstractThe combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.

scholarly journals Existence of a common solution to systems of integral equations via fixed point results

2020 ◽  
Vol 18 (1) ◽  
pp. 249-261
Author(s):  
Hüseyin Işık ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
System Of Integral Equations ◽  
Common Solution ◽  
Coupled Common Fixed Point ◽  
Systems Of Integral Equations

Abstract The goal of this article is to prove some coupled common fixed point results by using weakly increasing mappings with two variables. Several examples indicating the usability are provided. Also, we use the results obtained to demonstrate the existence of a common solution to a system of integral equations.

scholarly journals On the Existence of the Solutions for Some Nonlinear Volterra Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
İsmet Özdemir ◽  
Ümit Çakan ◽  
Bekir İlhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Functional Integral ◽  
Space Of Continuous Functions ◽  
Nonlinear Functional ◽  
Functional Integral Equations

We present a theorem which gives sufficient conditions for existence of at least one solution for some nonlinear functional integral equations in the space of continuous functions on the interval[0,a]. To do this, we will use Darbo's fixed-point theorem associated with the measure of noncompactness. We give also an example satisfying the conditions of our main theorem but not satisfying the conditions described by Maleknejad et al. (2009).

scholarly journals Global Existence of Solutions to a System of Integral Equations Related to an Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
System Of Integral Equations ◽  
Global Existence Of Solutions

A system of integral equations related to an epidemic model is investigated. Namely, we derive sufficient conditions for the existence and uniqueness of global solutions to the considered system. The proof is based on Perov’s fixed point theorem and some integral inequalities.

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