On a measure of noncompactness in the space of regulated functions and its applications

Abstract

In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Among others, it creates the basis to construct a regular measure of noncompactness in the space of regulated functions. We show the applicability of the constructed measure of noncompactness in proving the existence of solutions of a quadratic Hammerstein integral equation in the space of regulated functions.

Keywords

• space of regulated functions
• criterion of relative compactness
• measure of noncompactness
• fixed point theorem of darbo type
• quadratic hammerstein integral equation
• 26a45
• 47h08