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The Australian Journal of Mathematical Analysis and Applications ISSN 1449-5910 |
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Paper Title:
Stability of Almost Multiplicative Functionals
Author(s):
Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi
Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,
Japan
Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,
Japan
Department of Applied Mathematics and Physics, Graduate School of
Science and Engineering,
Yamagata University,
Yonezawa 992-8510
Japan
oka@mx.ibaraki.ac.jp
miura@yz.yamagata-u.ac.jp
sin-ei@emperor.yz.yamagata-u.ac.jp
Abstract:
Let
δ
and p be non-negative real numbers. Let
be the
real or complex number field and
a normed algebra
over . If a mapping
satisfies
then we show that
φ
is multiplicative or
for all 
If, in
addition,
φ
satisfies
for some p≠1, then by using Hyers-Ulam-Rassias
stability of additive Cauchy equation, we show that
φ
is a ring homomorphism or
for all
In other words,
φ
is a ring homomorphism, or an approximately zero
mapping. The results of this paper are inspired by Th.M. Rassias' stability
theorem.
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