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

ISSN : 3059-0604

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Vol.15 No.4

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ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A $C^*$-ALGEBRA

ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A C*-ALGEBRA

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2008, v.15 no.4, pp.393-400
An, Jong-Su (DEPARTMENT OF MATHEMATICS EDUCATION, PUSAN NATIONAL UNIVERSITY)
An, Jong-Su. (2008). ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A <TEX>$C^*$</TEX>-ALGEBRA, 15(4), 393-400.

Abstract

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||${\leq}$||f(x+y)+f(z+w)|| in normed modules over a $C^*$-algebra. This is applied to understand homomor-phisms in $C^*$-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||${\leq}$||f(x+y+z+w)||+${\theta}||x||^p||y||^p||z||^p||w||^p$ in real Banach spaces, where ${\theta}$, p are positive real numbers with $4p{\neq}1$.

keywords
Jordan-von Neumann functional equation, functional inequality, linear mapping in normed modules over a <tex> $C^*$</tex>-algebra

한국수학교육학회지시리즈B:순수및응용수학

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