A GENERALIZATION OF THE STABILITY OF A QUARTIC FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES WITH THE FIXED POINT METHOD

The stability of functional equations has been a central topic in mathematical analysis due to its significance in various fields, including approximation theory, dynamical systems, and optimization problems. In this paper, by utilizing the fixed point method, we investigate the Hyers-Ulam stability of one form of the quartic functional equation involving an unknown function from a normed space into a quasi-(3-Banach space. This approach not only provides constructive proof but also demonstrates the versatility of fixed point theory in solving stability problems. The results obtained in this study extend existing works on quartic functional equations and offer a more general framework applicable to quasi-(3-Banach spaces.