Stability Results of Autonomous and Non-singular Delay Difference Equations over Bounded and Unbounded Discrete Intervals

Abstract

This paper is about the Hyer-Ulam-Rassias stability of a non-singular and non-autonomous difference equation with delay. The details of Hyers-Ulam-rassias is given in the introdution. The main purpose of this paper is to generlaized the previuse results giev in Moonsuwan et al. (2022) from Hyers-Ulam to Hyers-Ulam_Rassias stability. In the first step, the stability results of the mentioned model are achieved over bounded discrete interval. Then in the next step, the corresponding results are achieved over unbounded discrete interval. Furthermore, this concept is extended to infinite impulses. The stability results are achieved with the help of  discrete Gronwall inequality. To deal with challenges and achieve desired outcomes, certain assumptions have been introduced.