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http://dx.doi.org/10.7468/jksmeb.2018.25.2.161

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

Park, Choonkil (Research Institute for Natural Sciences, Hanyang University)
Yun, Sungsik (Department of Financial Mathematics, Hanshin University)
Publication Information
The Pure and Applied Mathematics / v.25, no.2, 2018 , pp. 161-170 More about this Journal
Abstract
In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) 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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