S-asymptotically omega-periodic sequential solutions to difference equations

Abstract

In this paper, we introduce the concept of s-asymptotically $\omega$-periodic sequences. We prove some properties of these S-asymptotically $\omega$-periodic sequences, including a pair of discrete sums, one a finite convolution the other infinite. These sums are then utilized to find S-asymptotically $\omega$-periodic solutions of first order difference equations, linear and then semi-linear.