Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 188, pp. 1-20.

Title: Stepanov-like pseudo-almost automorphic functions in Lebesgue
       spaces with variable exponents $L^{p(x)}$

Authors: Toka Diagana   (Howard Univ., Washington, DC, USA)
         Mohamed Zitane (Univ. Ibn Tofail, Kenitra 1400, Maroc)

Abstract:
 In this article we introduce and study a new class of functions
 called Stepanov-like pseudo-almost automorphic functions with
 variable exponents, which generalizes in a natural way classical
 Stepanov-like pseudo-almost automorphic spaces. Basic properties
 of these new spaces are investigated. The existence of pseudo-almost
 automorphic solutions to some first-order differential equations with
 $S^{p,q(x)}$-pseudo-almost automorphic coefficients will also be studied.

Submitted May 23, 2013. Published August 28, 2013.
Math Subject Classifications: 34C27, 35B15, 46E30.
Key Words: Pseudo-almost automorphy; $S^{p,q(x)}$-pseudo-almost automorphic;
           Lebesgue space with variable exponents; variable exponents.