Solvability of an infinite system of integral equations on the real half-axis

• Main Authors: Banaś Józef, Woś Weronika
• Format: Article
• Language: English
• Published: De Gruyter 2020-06-01
• Series: Advances in Nonlinear Analysis
• Subjects: space of functions continuous and bounded on the half-axis; sequence space; measure of noncompactness; fixed point theorem of darbo type; infinite system of integral equations; primary 47h08; secondary 45g1
• Online Access: https://doi.org/10.1515/anona-2020-0114
• ISSN: 2191-9496; 2191-950X

The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.