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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.24 No.1

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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
2017, v.24 no.1, pp.21-31
https://doi.org/10.7468/jksmeb.2017.24.1.21
Yun, Sungsik
Shin, Dong Yun
Yun,, S. , & Shin,, D. Y. (2017). STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES. , 24(1), 21-31, https://doi.org/10.7468/jksmeb.2017.24.1.21

Abstract

In this paper, we introduce and solve the following additive (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality <TEX>∥2f(x+y2)−f(x)−f(y)∥≤∥ρ1(f(x+y)+f(x−y)−2f(x))∥+∥ρ2(f(x+y)−f(x)−f(y))∥

</TEX> where <TEX>${\rho}_1$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero complex numbers with <TEX>$\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$</TEX>. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (1) in complex Banach spaces.

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

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

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