Superstability of an Exponential Equation in C*-Algebras

作者：Kim Gwang Hui^*; Park Choonkil

来源：Results in Mathematics, 2015, 67(1-2): 197-205.

DOI：10.1007/s00025-014-0404-4

• Hyers-Ulam stability
• superstability
• C*-Algebra
• generalized Pexider exponential equation

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.

• 出版日期2015-2