Banach Journal of Mathematical Analysis

On solutions of an infinite system of nonlinear integral equations on the real half-axis

Józef Banaś and Agnieszka Chlebowicz

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Abstract

We investigate the existence of solutions of an infinite system of integral equations of Volterra–Hammerstein type on the real half-axis. The method applied in our study is connected with the construction of a suitable measure of noncompactness in the space of continuous and bounded functions defined on the real half-axis with values in the space c0 consisting of real sequences converging to zero and equipped with the classical supremum norm. We use the mentioned measure of noncompactness together with a fixed point theorem of Darbo type. Our investigations are illustrated by an example.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 4 (2019), 944-968.

Dates
Received: 27 August 2018
Accepted: 12 February 2019
First available in Project Euclid: 9 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1570608169

Digital Object Identifier
doi:10.1215/17358787-2019-0008

Mathematical Reviews number (MathSciNet)
MR4016904

Zentralblatt MATH identifier
07118769

Subjects
Primary: 47H08: Measures of noncompactness and condensing mappings, K-set contractions, etc.
Secondary: 45G15: Systems of nonlinear integral equations

Keywords
space of continuous and bounded functions defined on the half-axis sequence space measure of noncompactness fixed point theorem infinite system of integral equations

Citation

Banaś, Józef; Chlebowicz, Agnieszka. On solutions of an infinite system of nonlinear integral equations on the real half-axis. Banach J. Math. Anal. 13 (2019), no. 4, 944--968. doi:10.1215/17358787-2019-0008. https://projecteuclid.org/euclid.bjma/1570608169


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