[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2013.21.1.1

ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION

Lee, Jung Rye (Department of Mathematics Daejin University)
Lee, Sung Jin (Department of Mathematics Daejin University)
Park, Choonkil (Department of Mathematics Research Institute for Natural Sciences Hanyang University)

Publication Information

Korean Journal of Mathematics / v.21, no.1, 2013 , pp. 1-21 More about this Journal

Abstract

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$ (0.1) for all $x$ , $y$ , $z$ with $x{\bot}y$ , in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

Keywords

Ulam-Hyers stability; orthogonally additive and orthogonally quadratic functional equation; fixed point; non-Archimedean normed space; orthogonality space;

Citations & Related Records

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