On the generalized orthogonal stability of mixed type additive-cubic functional equations in modular spaces

Abstract

In this paper, we establish the Hyers-Ulam-Rassias stability of the mixed type additive-cubic functional equation $$f(2x+y)+f(2x-y)-f(4x)=2[f(x+y)+f(x-y)]-8f(2x)+10f(x)-2f(-x),$$ with $x\bot y,$ where $\bot $ is the orthogonality in the sense of Ratz in modular spaces.