On Stepanov-like almost periodicity in mixed Lebesgue spaces

F. Z. Ben Cheikh ; M. T. Khalladi ; M. Kostić

Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 47-58.

Résumé

The main purpose of this paper is to revisit the recently analyzed class of multi-dimensional Stepanov almost periodic functions. We introduce and study several new classes of Stepanov-like almost periodic functions in the mixed Lebesgue spaces. We also provide a new application of multi-dimensional Stepanov almost periodic functions to the abstract nonautonomous differential equations of first order, provided that all components of the exponent $\vec{p}\in [1,\infty)^{n}$ are equal.

Détail

Keywords: Stepanov-like almost periodic function in mixed Lebesgue space, multi-dimensional Stepanov almost periodic function, abstract nonautonomous differential equation of first order.

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