Measure pseudoasymptotically Bloch periodic functions in the sense of Stepanov and applications

Abstract

UDC 517.9 We focus on the measures of Stepanov-like pseudoasymptotically Bloch τ -periodicity and its applications. First, we define a new notion of measures of Stepanov-like pseudoasymptotically Bloch periodic functions and diccuss some of its fundamental properties. Then the obtained results are applied to investigate the existence and uniqueness of the measure Stepanov-like pseudoasymptotically Bloch periodic mild solutions to semilinear delay differential equation in Banach spaces. Finally, an application is presented to illustrate the efficiency of the results.