Solution and Stability of a Cubic Type Functional Equation: Using Direct and Fixed Point Methods

Abstract

In this concept, we investigate the generalized Ulam-Hyers-Rassias stability for the new type of cubic functional equation of the form g (ax 1 + bx 2 + 2cx 3) + g (ax 1 + bx 2 − 2cx 3) + 8 a 3 g(x 1) + 8 b 3 g(x 2) =2g(ax 1 + bx 2) + 4 (g(ax 1 + cx 3) + g(ax 1 − cx 3) + g(bx 2 + cx 3) + g(bx 2 − cx 3)) by using direct and fixed point alternative.

Stability of an l-Variable Cubic Functional Equation

“…Random theory has much application in several fields, for example, population dynamics, computer programming, nonlinear dynamical system, nonlinear operators, statistical convergence and so forth. The Cauchy additive equation has been studied by many authors [7,9,13,15,19]. The functional equation…”

Hyers–Ulam Stability of an Additive-Quadratic Functional Equation

“…Hyers theorem was generalized by Aoki [3] for additive mappings and Rassias [12] for quadratic mappings. During the last three decades the stability theorem of Rassias [26] provided a lot of influence for the development of stability theory of a large variety of functional equations (see [1,2,4,7,9,11,14,17,18,21,22,23,27]). One of the most famous functional equations is the following additive functional equation g(x + y) = g(x) + g(y)…”

Hyers-Ulam stability of an additive-quadratic functional equation

“…Hyers theorem was generalized by Aoki [3] for additive mappings and Rassias [12] for quadratic mappings. During the last three decades the stability theorem of Rassias [26] provided a lot of influence for the development of stability theory of a large variety of functional equations (see [1,2,4,7,9,11,14,17,18,21,22,23,27]). One of the most famous functional equations is the following additive functional equation g(x + y) = g(x) + g(y)…”