scholarly journals Existence of solutions for a class of system of functional integral equation via measure of noncompactness

2017 ◽  
Vol 313 ◽  
pp. 129-141 ◽  
Author(s):  
Jamal Rezaei Roshan
Keyword(s):  
Integral Equation ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral

scholarly journals Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral

2017 ◽  
Vol 9 (5) ◽  
pp. 46
Author(s):  
Hui Mei ◽  
Guoju Ye ◽  
Wei Liu ◽  
Yanrong Chen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Stieltjes Integral

In this paper, we apply the method associated with the technique of measure of noncompactness and some generalizations of Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile, an example is provided to illustrate our results.

scholarly journals On the existence of solutions for non-linear functional integral equation

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 17-23
Author(s):  
E.M. El-Abd
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo Fixed Point Theorem

We have proved the existence of monotonic solutions of a nonlinear functional integeral equation by using Darbo fixed point theorem associated with a measure of noncompactness.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals On a measure of noncompactness in the space of regulated functions and its applications

2018 ◽  
Vol 8 (1) ◽  
pp. 1099-1110 ◽  
Author(s):  
Józef Banaś ◽  
Tomasz Zając
Keyword(s):  
Integral Equation ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Closed Interval ◽  
Hammerstein Integral Equation ◽  
Regular Measure ◽  
Relative Compactness ◽  
Regulated Functions

Abstract In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Among others, it creates the basis to construct a regular measure of noncompactness in the space of regulated functions. We show the applicability of the constructed measure of noncompactness in proving the existence of solutions of a quadratic Hammerstein integral equation in the space of regulated functions.

scholarly journals Global Asymptotic Stability for Nonlinear Functional Integral Equation of Mixed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhinan Xia
Keyword(s):  
Integral Equation ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Equation Of Mixed Type ◽  
Stability Of The Solution

The existence results of global asymptotic stability of the solution are proved for functional integral equation of mixed type. The measure of noncompactness and the fixed-point theorem of Darbo are the main tools in carrying out our proof. Furthermore, some examples are given to show the efficiency and usefulness of the main findings.

scholarly journals Solvability of functional-integral equations (fractional order) using measure of noncompactness

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

scholarly journals A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

2021 ◽  
pp. 321
Author(s):  
Kourosh Nourouzi ◽  
Faezeh Zahedi ◽  
Donal O'Regan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Volterra Type

In this paper, we give a nonlinear F-contraction form of the Sadovskii fixedpoint theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.

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