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

Shim, EunHwa; Shim, EunHwa

doi:10.7468/jksmeb.2017.24.4.243

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P-ISSN3059-0604
E-ISSN3059-1309
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ISSN : 3059-0604

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Vol.24 No.4

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

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

한국수학교육학회지시리즈B:순수및응용수학 / 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.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, 24(4), 243-251, https://doi.org/10.7468/jksmeb.2017.24.4.243

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Abstract

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (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 ρ-FUNCTIONAL EQUATIONS IN β-HOMOGENEOUS F-SPACES

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학