scholarly journals Application of fixed point theorem of convex-power operators to nonlinear Volterra type integral equations

2014 ◽  
Vol 9 ◽  
pp. 407-417 ◽  
Author(s):  
Yan Chao-dong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Volterra Type ◽  
Type Integral

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 [

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals On a System of Volterra Type Hadamard Fractional Integral Equations in Fréchet Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
The Fixed Point Theorem ◽  
Hadamard Fractional Integral

In this article we present some results concerning the existence of solutions for a system of Hadamard integral equations. Our investigation is conducted with an application of an extension of the fixed point theorem of Burton-Kirk in Fréchet spaces.

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.

Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity

2013 ◽  
Vol 56 (1) ◽  
pp. 80-91
Author(s):  
Muhammad N. Islam
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Direct Method ◽  
Banach Fixed Point Theorem ◽  
Volterra Type ◽  
Type Integral

AbstractIn this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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