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

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.