Hyers-Ulam Stability of Quadratic Functional Equations in Random Normed Spaces

Abstract

This paper investigates the stability of quadratic functional equations in the context of random normed spaces using direct and fixed point method. Motivated by applications in functional analysis, we consider the behavior of solutions to quadratic functional equations under perturbations induced by random norms. Utilizing techniques from functional analysis, and stability theory, we establish conditions for the existence and uniqueness of solutions to these equations in random normed spaces.