A Fixed Point Approach to the Stability of a Functional Equation

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 4,  2010, pp.557-564
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.4.557
Title & Authors
A Fixed Point Approach to the Stability of a Functional Equation
Park, Won-Gil; Bae, Jae-Hyeong;

Abstract
By using an idea of C$\small{\u{a}}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $\small{f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}}$ given by f(x, y) = $\small{ax^2\;+\;by^2}$ is a solution of the above functional equation.
Keywords
Alternative of fixed point;Functional equation;Stability;
Language
English
Cited by
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