Hyers-Ulam Stability of Bessel Equations

TL;DR

This paper investigates various stability properties of Bessel and modified Bessel equations, providing sufficient conditions for different types of Hyers-Ulam stability using integral techniques.

Contribution

It introduces new sufficient conditions for Hyers-Ulam and related stabilities of Bessel equations based on integral methods.

Findings

Established conditions for Hyers-Ulam stability of Bessel equations.

Extended stability analysis to modified Bessel equations.

Utilized integral techniques to derive stability criteria.

Abstract

We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations. Those sufficient conditions are obtained based on the use of integral techniques and majorations.