Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 4 (2019), 944-968.
On solutions of an infinite system of nonlinear integral equations on the real half-axis
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 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.
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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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