Hyers-Ulam Stability of Quadratic Functional Equation in Modular Spaces

Abstract

In this research paper, we introduce a new quadratic functional equation and determine its general solution. Under suitable assumptions on the modular, we establish the Hyers–Ulam stability of this equation in modular spaces by direct method. These results extend classical stability theorems for quadratic mappings to the modular-spaces. Additionally, we present a counter example demonstrating the instability of the equation in certain cases.