Stepanov type weighted pseudo almost automorphic sequences and their applications to difference equations

Abstract

In this paper, we shall define the concept of Stepanov type weighted pseudo almost automorphic sequence and prove some basic results like composition theorem. Further, we investigate the existence, uniqueness of Stepanov type weighted pseudo almost automorphic sequence solutions to a difference equation as an application. The result obtained extends the theory of pseudo and weighted pseudo almost automorphic sequences to more general class of Stepanov type weighted pseudo almost automorphic sequence.