Additive p-functional Equations in β-homogeneous F-spaces

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2017, v.24 no.4, pp.243-251

https://doi.org/10.7468/jksmeb.2017.24.4.243

Shim, EunHwa (Department of Mathematics, Hanyang University)

Shim, EunHwa. (2017). ADDITIVE ρ-FUNCTIONAL EQUATIONS IN β-HOMOGENEOUS F-SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 24(4), 243-251, https://doi.org/10.7468/jksmeb.2017.24.4.243

복사

Abstract

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

keywords: Hyers-Ulam stability, <tex> ${\beta}-homogeneous$</tex> F-space, additive <tex> ${\rho}-functional$</tex> equation

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논문 상세

Vol.24 No.4

ADDITIVE &#961;-FUNCTIONAL EQUATIONS IN &#946;-HOMOGENEOUS F-SPACES

Additive p-functional Equations in β-homogeneous F-spaces

Abstract

한국수학교육학회지시리즈B:순수및응용수학

ADDITIVE ρ-FUNCTIONAL EQUATIONS IN β-HOMOGENEOUS F-SPACES