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ISSN : 1226-0657

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Vol.25 No.2
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HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2018, v.25 no.2, pp.161-170
https://doi.org/10.7468/jksmeb.2018.25.2.161
Park, Choonkil
Yun, Sungsik
Park,, C. , & Yun,, S. (2018). HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(2), 161-170, https://doi.org/10.7468/jksmeb.2018.25.2.161
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Abstract

In this paper, we introduce and solve the following additive (<TEX>${\rho}_1,{\rho}_2$</TEX>)-functional inequality (0.1) <TEX>$${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$</TEX>, where <TEX>${\rho}_1$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero complex numbers with <TEX>${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$</TEX> < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (<TEX>${\rho}_1,{\rho}_2$</TEX>)-functional inequality (0.1) in complex Banach spaces.

keywords
Hyers-Ulam stability, additive (<tex> ${\rho}_1, {\rho}_2$</tex>)-functional inequality, fixed point method, direct method, Banach space

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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