Application of contraction mapping principle to the Hyers-Ulam-Rassias stability problem of pexiderized quadratic functional equation in modular spaces

Abstract

In this paper, the Hyers-Ulam-Rassias stability property for a pexiderized quadratic functional equation is investigated. The framework of the study is modular spaces. The type of stability considered in this paper has a very general nature for which it has been studied in diverse domains of mathematics. Here we establish our result by applying fixed point technique. For that purpose, we use an extension of Banach's contraction mapping principle to modular metric spaces. A speciality of our result is that it is established without the assumption of $\Delta_2$ property for which we have to deal with functional equations for odd and even functions separately. The present research is in the domain of stability studies of functional equations, more specifically, in the domain of such studies in modular spaces which is a recently developed domain of mathematics.