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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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