WEIGHTED STEPANOV-LIKE PSEUDO-ALMOST PERIODIC FUNCTIONS IN LEBESGUE SPACE WITH VARIABLE EXPONENTS Lp(x).

In this paper we introduce and study a new class of functions called S p,q(x)-pseudoalmost periodic (or weighted Stepanov-like pseudo-almost periodic functions with variable exponents), which generalizes the class of weighted Stepanov-like pseudoalmost periodic functions. Basic properties of these new spaces are established. The existence of weighted pseudo-almost periodic solutions to some first-order differential equations with S p,q(x)-pseudo-almost periodic coefficients will also be studied. [ABSTRACT FROM AUTHOR]