Title & Authors
Roh, Jai-Ok; Shin, Hui-Joung;

Abstract
In this paper, we prove that a function satisfying the following inequality $\small{{\parallel}f(x)+2f(y)+2f(z){\parallel}{\leq}{\parallel}2f(\frac{x}{2}+y+z){\parallel}+{\epsilon}({\parallel}x{\parallel}^r{\cdot}{\parallel}y{\parallel}^r{\cdot}{\parallel}z{\parallel}^r)}$ for all x, y, z $\small{{\in}}$ X and for $\small{\epsilon{\geq}0}$, is Cauchy additive. Moreover, we will investigate for the stability in Banach spaces.
Keywords
Hyers-Ulam stability;Cauchy additive mapping;Jordan-von Neumann type Cauchy Jensen functional equation;
Language
English
Cited by
1.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS,;;

대한수학회보, 2010. vol.47. 1, pp.195-209
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Functional Inequalities Associated with Additive Mappings, Abstract and Applied Analysis, 2008, 2008, 1
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CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 1
3.
A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation, Fixed Point Theory and Applications, 2009, 2009, 1, 918785
4.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 195
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