Fixed Point Technique: Stability Analysis of Quadratic Functional Equation in Various Quasi-Banach Spaces

Abstract

In this present work, we derive the solution of a quadratic functional equation and investigate the Ulam stability of this equation in Banach spaces using fixed point and direct techniques. Mainly, we examine the stability results in quasi-β-Banach spaces and quasi-fuzzy β-Banach spaces by means of direct method as well as quasi-Banach spaces by means of alternative fixed point theorem in the sense of generalized b-metric spaces. To further establish the instability of a single case, an appropriate counterexample is also provided.