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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.24 No.4

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Shim,, E. (2017). Additive p-functional Equations in β-homogeneous F-spaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 24(4), 243-251, https://doi.org/10.7468/jksmeb.2017.24.4.243

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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