Hyers--Ulam stability for Hammerstein integral equations with impulses and delay

Abstract

This paper mainly focuses on solving the Hyers--Ulam and Hyers--Ulam--Rassias stability problem of the Hammerstein integral equation with impulses and delay using fixed point technique. The consequent different cases of a finite interval and an infinite interval are studied. Finally, a concrete example is given at the end to justify the efficiency of the obtained theoretical results.