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december 2015 Construction of compact-integral operators on $BC(\Omega)$ with application to the solvability of functional integral equations
Reza Allahyari, Reza Arab, Ali Shole Haghighi
Bull. Belg. Math. Soc. Simon Stevin 22(5): 761-779 (december 2015). DOI: 10.36045/bbms/1450389247

Abstract

In this article, using the concept of measure of noncompactness, we give some results concerning the compactness and continuity of the nonlinear Volterra and Fredholm integral operators on the space $ BC(\Omega)$ ($\Omega$ is an unbounded subset of the Euclidean space $\Bbb{R}^n$). Then, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results generalize and improve some previous works. We will also include some examples which show that our results are applicable where the previous ones are not.

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Reza Allahyari. Reza Arab. Ali Shole Haghighi. "Construction of compact-integral operators on $BC(\Omega)$ with application to the solvability of functional integral equations." Bull. Belg. Math. Soc. Simon Stevin 22 (5) 761 - 779, december 2015. https://doi.org/10.36045/bbms/1450389247

Information

Published: december 2015
First available in Project Euclid: 17 December 2015

zbMATH: 1330.47094
MathSciNet: MR3435081
Digital Object Identifier: 10.36045/bbms/1450389247

Subjects:
Primary: 34A12 , 47H09 , 47H10

Keywords: Compact-integral operators , fixed point , Functional integral equations , measure of noncompactness

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 5 • december 2015
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