Bulletin of the Belgian Mathematical Society - Simon Stevin

Construction of compact-integral operators on $BC(\Omega)$ with application to the solvability of functional integral equations

Reza Allahyari, Reza Arab, and Ali Shole Haghighi

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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.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 5 (2015), 761-779.

First available in Project Euclid: 17 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Measure of noncompactness Functional integral equations Fixed point Compact-integral operators


Allahyari, Reza; Arab, Reza; Haghighi, Ali Shole. Construction of compact-integral operators on $BC(\Omega)$ with application to the solvability of functional integral equations. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 5, 761--779. doi:10.36045/bbms/1450389247. https://projecteuclid.org/euclid.bbms/1450389247

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