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.

scholarly journals Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 492
Author(s):  
Babak Mohammadi ◽  
Ali Asghar Shole Haghighi ◽  
Maryam Khorshidi ◽  
Manuel De la Sen ◽  
Vahid Parvaneh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals Solvability of a system of integral equations of Volterra type in the Fréchet space lp loc(R+) via measure of noncompactness

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5255-5263 ◽  
Author(s):  
Shahram Banaei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
Fréchet Space ◽  
Volterra Type ◽  
System Of Integral Equations

The purpose of this article is to analyze the existence of solutions for a system of integral equations of Volterra type in the Fr?chet space Lp loc(R+) and prove a fixed point theorem of Darbo-type in this space. The technique of measure of noncompactness by applying fixed point theorem is the main tool in carrying out our proof. Moreover, we present an example to show the efficiency of our results.

scholarly journals On New Extensions of Darbo’s Fixed Point Theorem with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 424 ◽  
Author(s):  
Hüseyin Işık ◽  
Shahram Banaei ◽  
Farhan Golkarmanesh ◽  
Vahid Parvaneh ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals On solvability of infinite system of integral equations of Volterra together with Hammerstein type in the Fréchet spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2055-2069
Author(s):  
Shahram Banaei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
System Of Integral Equations

In this paper, we prove some fixed point theorems associated with Tychonoff fixed point theorem and measure of noncompactness in the Fr?chet spaces. Moreover, as an application of our results, we analyze the existence of solutions for infinite system of integral equations of Volterra together with Hammerstein type. Finally, we present an example to illustrate the effectiveness of our results.

scholarly journals Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Sufficient Conditions ◽  
Fredholm Integral Equations ◽  
Equations Of Mixed Type ◽  
Stochastic Integral Equations

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

Global solutions for Volterra ordinary and retarded integral equations

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Bianca Satco
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Global Solutions ◽  
Volterra Type ◽  
Darbo’S Fixed Point Theorem ◽  
Type Integral

AbstractUsing a generalization of Darbo’s fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

Sign in / Sign up

Export Citation Format

Share Document