The Hyers-Ulam stability for nonlinear Volterra integral equations via a generalized Diaz-Margolis's fixed point theorem

TL;DR

This paper establishes the Hyers-Ulam stability for nonlinear Volterra integral equations by extending existing theorems with weaker assumptions, using a generalized fixed point theorem.

Contribution

It introduces a generalized Diaz-Margolis's fixed point theorem to prove stability results under less restrictive conditions.

Findings

Proved Hyers-Ulam stability for a broad class of nonlinear Volterra equations.

Extended Castro-Ramos theorem with weaker conditions.

Provided a new methodological approach using fixed point theory.

Abstract

In this work, we prove an existence theorem of the Hyers-Ulam stability for the nonlinear Volterra integral equations which improves and generalizes Castro-Ramos theorem by using some weak conditions.