An approximate mixed type quadratic and quintic functional equation in various Banach spaces

Abstract

In this paper, the general solutions of a mixed type quadratic and quintic functional equation are obtained. In fact, it is shown under which conditions, the mentioned functional equation can be either quadratic or quintic. Moreover, some Ulam-Hyers-Rassias stability results of a mixed quadratic and quintic functional equation are established in various Banach spaces by using (Hyers) direct and fixed point methods. In other words, by applying an alternative fixed point theorem, we give a control function to investigate Gavruta and Rassias stability to approximate the solution of the mentioned equation with quality and certainty of the approximation by using the concept of generalized Z-numbers.