The purpose of this paper is to obtain refined stability results and alternative stability results for additive and quadratic functional equations using direct method in modular spaces.

In this article, we present generalized Hyers–Ulam stability results of a cubic functional equation associated with an approximate cubic Lie derivations on convex modular algebras χρ with Δ2-condition on the convex modular functional ρ.

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In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers-Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces.

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equationin quasi-Banach space and non-Archimedean space, where r = ±1, 0 and s are real numbers.