On the stability of orthogonally Jensen additive and quadratic functional equation

TL;DR

This paper investigates the stability of orthogonal Jensen additive and quadratic functional equations in F-spaces, introducing a new method that extends previous results under more general conditions.

Contribution

It presents a novel approach to stability analysis of these equations, broadening the applicable conditions beyond prior work.

Findings

Established new stability results for orthogonal Jensen equations

Extended the stability framework to more general conditions

Provided a new methodological approach for functional equation stability

Abstract

We consider the stability of the orthogonal Jensen additive and quadratic equations in $F$-spaces, through applying and extending the approach to the proof of a 2010 result of W.Frchner and J.Sikorska, we presenting a new method to get the stability. Moreover, we work in a more general and natural condition than considered before by other antuors.