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http://dx.doi.org/10.5666/KMJ.2010.50.4.557

A Fixed Point Approach to the Stability of a Functional Equation  

Park, Won-Gil (Department of Mathematics Education, College of Education, Mokwon University)
Bae, Jae-Hyeong (College of Liberal Arts, Kyung Hee University)
Publication Information
Kyungpook Mathematical Journal / v.50, no.4, 2010 , pp. 557-564 More about this Journal
Abstract
By using an idea of C$\u{a}$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 $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.
Keywords
Alternative of fixed point; Functional equation; Stability;
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Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
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