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

ISSN : 3059-0604

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Vol.23 No.3

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Additive ρ-functional inequalities in β-homogeneous F-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
2016, v.23 no.3, pp.319-328
https://doi.org/10.7468/jksmeb.2016.23.3.319
LEE, HARIN
CHA, JAE YOUNG
CHO, MIN WOO
KWON, MYUNGJUN
LEE,, H. , CHA,, J. Y. , CHO,, M. W. , & KWON,, M. (2016). Additive ρ-functional inequalities in β-homogeneous F-spaces, 23(3), 319-328, https://doi.org/10.7468/jksmeb.2016.23.3.319

Abstract

In this paper, we solve the additive ρ-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| $\leq$ ||${\rho}(f(x+y)-f(x)-f(y))$||, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ||f(x+y)-f(x)-f(y)|| $\leq$ ||${\rho}(f(2x-y)-f(y-x)-f(x))$||, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in β-homogeneous F-spaces.

keywords
Hyers-Ulam stability, β-homogeneous F-space, additive ρ-functional inequality

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

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