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

ISSN : 3059-0604

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Vol.10 No.3

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LINEAR MAPPINGS, QUADRATIC MAPPINGS AND CUBIC MAPPINGS IN NORMED SPACES

LINEAR MAPPINGS, QUADRATIC MAPPINGS ANDCUBIC MAPPINGS IN NORMED SPACES

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2003, v.10 no.3, pp.185-192
Park, Chun-Gil (Department of Mathematics, Chunganam National University)
Wee, Hee-Jung (Department of Mathematics, Chungnam National University)
Park, Chun-Gil, & Wee, Hee-Jung. (2003). LINEAR MAPPINGS, QUADRATIC MAPPINGS AND CUBIC MAPPINGS IN NORMED SPACES, 10(3), 185-192.

Abstract

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

keywords
liner mapping, quadratic mapping, cubic mapping, stability

한국수학교육학회지시리즈B:순수및응용수학

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