Different stabilities for oscillatory Volterra integral equations

Abstract

Inspired by the increasing development of theories subordinate to the topic of stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias, we present in this paper new sufficient conditions for concluding the stability of classes of integral equations with kernels depending on sine and cosine functions. This will be done by taking the profit of fixed‐point arguments in the framework of spaces of continuous functions endowed with a generalization of the Bielecki metric. After presenting the main theorems, some examples are provided to verify the effectiveness of the proposed theoretical results.