Almost additive-quadratic-cubic mappings in modular spaces

Abstract

We introduce and obtain the general solution of a class of generalized mixed additive, quadratic and cubic functional equations. We investigate the stability of such modified functional equations in the modular space Xρ by applying the ∆ 2-condition and the Fatou property (in some results) on the modular function ρ. Furthermore, a counterexample for the even case (quadratic mapping) is presented.

Two multi-cubic functional equations and some results on the stability in modular spaces

“…Furthermore, a refined stability result and alternative stability results for additive and quadratic functional equations using the direct method in modular spaces are given in [21]. For the stability of mixed additive-quadratic-cubic mappings in modular spaces which were recently studied, we refer to [25].…”