Some inequalities and superposition operator in the space of regulated functions

Abstract

Some inequalities connected to measures of noncompactness in the space of regulated function R(J, E) were proved in the paper. The inequalities are analogous of well known estimations for Hausdorff measure and the space of continuous functions. Moreover two sufficient and necessary conditions that superposition operator (Nemytskii operator) can act from R(J, E) into R(J, E) are presented. Additionally, sufficient and necessary conditions that superposition operator Ff : R(J, E) → R(J, E) was compact are given.

Keywords

• space of regulated functions
• measure of noncompactness
• integral inequalities
• superposition operator
• primary 47h30
• secondary 46e40