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In this paper, we study the stability of the orthogonal equation,which isclosely related to the results by Wlodzimierz Fechner and Justyna Sikorska in2010. There are some differences that we consider the target space with the\b{eta}-homogeneous norm and quasi-norm. Overcoming the \b{eta}-homogeneousnorm and quasi-norm bottlenecks, we get some new results.

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