On the stability of orthogonal additivity in $\beta$-homogeneous $F$-spaces and quasi-Banach spaces

TL;DR

This paper investigates the stability of the orthogonal equation within ta-homogeneous $F$-spaces and quasi-Banach spaces, extending previous results by addressing challenges posed by these generalized norms.

Contribution

It introduces new stability results for the orthogonal equation in ta-homogeneous and quasi-normed spaces, expanding the scope of prior work.

Findings

Established stability conditions in ta-homogeneous $F$-spaces.

Extended stability analysis to quasi-Banach spaces.

Overcame technical challenges related to ta-homogeneous norms and quasi-norms.

Abstract

In this paper, we study the stability of the orthogonal equation,which is closely related to the results by Wlodzimierz Fechner and Justyna Sikorska in 2010. There are some differences that we consider the target space with the \b{eta}-homogeneous norm and quasi-norm. Overcoming the \b{eta}-homogeneous norm and quasi-norm bottlenecks, we get some new results.