Superstability of an Exponential Equation in C*-Algebras
- Authors
- Kim, Gwang Hui; Park, Choonkil
- Issue Date
- Feb-2015
- Publisher
- SPRINGER BASEL AG
- Keywords
- Hyers-Ulam stability; superstability; C*-Algebra; generalized Pexider exponential equation
- Citation
- RESULTS IN MATHEMATICS, v.67, no.1-2, pp.197 - 205
- Indexed
- SCIE
SCOPUS
- Journal Title
- RESULTS IN MATHEMATICS
- Volume
- 67
- Number
- 1-2
- Start Page
- 197
- End Page
- 205
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/143851
- DOI
- 10.1007/s00025-014-0404-4
- ISSN
- 1422-6383
- Abstract
- The aim of this paper is to prove the superstability of the following functional equations f(x+y/m)(m) = g(x)h(y), where f,g,h : V-2 -> A are unknown mappings and m is a fixed positive integer. Here V is a vector space, and A is a unital normed algebra. Furthermore, we prove the superstability of the following generalized Pexider exponential equation f(x+y/r)(r) = g(x)h(y), where f, g, h : V-2 -> I(A) boolean AND A(+) are unknown mappings and r is a fixed nonzero rational number. Here V is a vector space, I(A) is the set of all invertible elements in a commutative unital C*-algebra A and A(+) is the positive cone of A.
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