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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Research Institute for Natural Sciences, Hanyang University)
Yun, Sungsik (Department of Financial Mathematics, Hanshin University)

Park, Choonkil, & Yun, Sungsik. (2018). HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 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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Vol.25 No.2

HYERS-ULAM STABILITY OF AN ADDITIVE (ρ<sub>1</sub>, ρ<sub>2</sub>)-FUNCTIONAL INEQUALITY IN BANACH SPACES

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학

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논문 상세

Vol.25 No.2

HYERS-ULAM STABILITY OF AN ADDITIVE (&#961;<sub>1</sub>, &#961;<sub>2</sub>)-FUNCTIONAL INEQUALITY IN BANACH SPACES

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학

HYERS-ULAM STABILITY OF AN ADDITIVE (ρ<sub>1</sub>, ρ<sub>2</sub>)-FUNCTIONAL INEQUALITY IN BANACH SPACES