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http://dx.doi.org/10.7468/jksmeb.2017.24.1.21

STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES  

Yun, Sungsik (Department of Financial Mathematics, Hanshin University)
Shin, Dong Yun (Department of Mathematics, University of Seoul)
Publication Information
The Pure and Applied Mathematics / v.24, no.1, 2017 , pp. 21-31 More about this Journal
Abstract
In this paper, we introduce and solve the following additive (${\rho}_1$, ${\rho}_2$)-functional inequality $${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$ where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with $\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1$, ${\rho}_2$)-functional inequality (1) in complex Banach spaces.
Keywords
Hyers-Ulam stability; additive (${\rho}_1$, ${\rho}_2$)-functional inequality; fixed point method; direct method; Banach space;
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