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July 2017 On the existence of at least a solution for functional integral equations via measure of noncompactness
Calogero Vetro, Francesca Vetro
Banach J. Math. Anal. 11(3): 497-512 (July 2017). DOI: 10.1215/17358787-2017-0003

Abstract

In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation

u(t)=g(t,u(t))+0tG(t,s,u(s))ds,t[0,+[, in the space of all bounded and continuous real functions on R+, under suitable assumptions on g and G. Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.

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Calogero Vetro. Francesca Vetro. "On the existence of at least a solution for functional integral equations via measure of noncompactness." Banach J. Math. Anal. 11 (3) 497 - 512, July 2017. https://doi.org/10.1215/17358787-2017-0003

Information

Received: 18 June 2016; Accepted: 28 July 2016; Published: July 2017
First available in Project Euclid: 19 April 2017

zbMATH: 06754300
MathSciNet: MR3679893
Digital Object Identifier: 10.1215/17358787-2017-0003

Subjects:
Primary: 47H08
Secondary: 45N05, 54H25

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.11 • No. 3 • July 2017
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