The article introduces and studies the concept of p-mean almost periodicity for stochastic processes. Our abstract results are, subsequently, applied to studying the existence of squaremean almost periodic solutions to some semilinear stochastic equations.
In this paper we introduce and analyze an important class of (asymptotically)
Stepanov almost periodic functions in the Lebesgue spaces with variable
exponents, which generalizes in a natural fashion all the (asymptotically)
almost periodic functions. We then make extensive use of these new functions
to study some abstract Volterra integro-differential equations in Banach
spaces including multi-valued ones.
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