The stability of a quadratic type functional equation with the fixed point alternative

TL;DR

This paper establishes the general solution and stability of a quadratic functional equation using fixed point methods, extending the understanding of such equations' behavior and stability properties.

Contribution

It introduces a novel approach to analyze the stability of quadratic functional equations via the fixed point alternative, providing new solutions and stability results.

Findings

Derived the general solution for the quadratic functional equation.

Proved Hyers-Ulam-Rassias stability using fixed point techniques.

Extended stability analysis to fixed integers c with c≠0,±1.

Abstract

In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability for the quadratic type functional equation &f(x+y+2cz)+f(x+y-2cz)+c^2f(2x)+c^2f(2y) &=2[f(x+y)+c^2f(x+z)+c^2f(x-z)+c^2f(y+z)+c^2f(y-z)] {2.6 cm} for fixed integers $c$ with $c\neq0,\pm1$, by using the fixed point alternative.