scholarly journals A Cone Measure of Noncompactness and Some Generalizations of Darbo’s Theorem with Applications to Functional Integral Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Mohamed Jleli ◽  
Mohammad Mursaleen ◽  
Kishin Sadarangani ◽  
Bessem Samet
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Functional Integral Equations ◽  
Cone Measure

We introduce the concept of cone measure of noncompactness and obtain some generalizations of Darbo’s theorem via this new concept. As an application, we establish an existence theorem for a system of integral equations. An example is also provided to illustrate the obtained result.

scholarly journals Application of measure of noncompactness for the system of functional integral equations

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3063-3073 ◽  
Author(s):  
Reza Arab
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Darbo Fixed Point Theorem ◽  
Functional Integral Equations

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banch space via the measure of non-compactness, which generalize the result of Aghajani et al.[6]. Our results generalize, extend, and unify several well-known comparable results in the literature. As an application, we study the existence of solutions for the system of integral equations.

scholarly journals Solvability for generalized nonlinear two dimensional functional integral equations via measure of noncompactness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soniya Singh ◽  
Bhupander Singh ◽  
Kottakkaran Sooppy Nisar ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Two Dimensional ◽  
Functional Integral Equations

AbstractIn this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the corresponding results of several authors. We present fascinating examples of equations.

scholarly journals Comment on “Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels”

2015 ◽  
Vol 2015 ◽  
pp. 1-3
Author(s):  
Krzysztof A. Topolski
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Functional Integral ◽  
Discontinuous Kernels ◽  
Functional Integral Equations

We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way.

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.

Some existence results and stability concepts for partial fractional random integral equations with multiple delay

2018 ◽  
Vol 26 (1) ◽  
pp. 53-63
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Random Fixed Point ◽  
Multiple Delay ◽  
The Stability ◽  
Random Integral ◽  
Random Fixed Point Theorem ◽  
Functional Integral Equations ◽  
Stability Concepts

Abstract In this paper, we present some results concerning the existence and the stability of solutions for some functional integral equations of Riemann–Liouville fractional order with random effects and multiple delay, by applying a random fixed point theorem with stochastic domain and the measure of noncompactness.

scholarly journals Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 214 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Control Function ◽  
Functional Integral ◽  
Existence Of A Solution ◽  
And Control ◽  
Functional Integral Equations

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

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