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

Youssef Khemili; Mohsen Miraoui; Mounir Ben Salah

doi:10.3842/umzh.v74i4.7339

Youssef Khemili FSS, Sfax University, Tunisia
Mohsen Miraoui IPEIK, Kairouan University, Tunisia
Mounir Ben Salah IPEIK, Kairouan University, Tunisia

DOI: https://doi.org/10.3842/umzh.v74i4.7339

Keywords: Stepanov-like pseudo-asymptotically Bloch periodic functions; positive measure; nonlinear differential equation; fixed point theorem.

Abstract

UDC 517.9

We focus on the measures of Stepanov-like pseudoasymptotically Bloch $\tau$-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.

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