Superstability of an Exponential Equation in C*-Algebras

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.