ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

Paokanta, Siriluk; Paokanta, Siriluk; Shim, Eon Hwa; Shim, Eon Hwa

doi:10.7468/jksmeb.2018.25.3.219

P-ISSN3059-0604
E-ISSN3059-1309
KCI

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ISSN : 3059-0604

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Vol.25 No.3

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ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2018, v.25 no.3, pp.219-227

https://doi.org/10.7468/jksmeb.2018.25.3.219

Paokanta, Siriluk (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University)
Shim, Eon Hwa (Department of Mathematics, Daejin University)

Paokanta, Siriluk, & Shim, Eon Hwa. (2018). ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE. , 25(3), 219-227, https://doi.org/10.7468/jksmeb.2018.25.3.219

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Abstract

In this paper, we solve the additive <TEX>${\rho}$</TEX>-functional equations <TEX>

$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$ </TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < 1, and <TEX>

$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$ </TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive <TEX>${\rho}$</TEX>-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

keywords: Hyers-Ulam stability, non-Archimedean normed space, additive <tex> ${\rho}$</tex>-functional equation

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Vol.25 No.3

ADDITIVE &#961;-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

Abstract

한국수학교육학회지시리즈B:순수및응용수학

ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE