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

Park, Choonkil; Park, Choonkil; Yun, Sungsik; Yun, Sungsik

doi:10.7468/jksmeb.2018.25.2.161

P-ISSN3059-0604
E-ISSN3059-1309
KCI

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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: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

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. , 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

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Article Contents

Vol.25 No.2

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

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics