A fixed point approach to the stability of a quadratic functional equation in modular spaces without ∆2-conditions
Abstract
In this paper we explore the Hyers-Ulam-Rassias stability property of a quadratic
functional equation. Even and odd cases for the corresponding function are treated
separately before combining them into a single stability result. The study is under-
taken in the relatively new structure of modular spaces. The theorems are deduced
without the use of the familiar ∆2-property of that space. This has rendered the proofs complicated. A fixed point methodology is adopted in the proofs for which a modular space version of the Banach's contraction mapping principle is utilized. There are several corollaries and an illustrative example.