ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A C*-ALGEBRA
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In this paper, we investigate the following additive functional inequality kf(x) + f(y) + f(z) + f(w)k · kf(x + y) + f(z + (0.1) w)k in normed modules over a C¤-algebra. This is applied to understand homomor-phisms in C¤-algebras. Moreover, we prove the generalized Hyers-Ulam stability of the functional in- equality (0.2) kf(x) + f(y) + f(z) + f(w)k · kf(x + y + z + w)k + µjjxjjpjjyjjpjjzjjpjjwjjp in real Banach spaces, where µ; p are positive real numbers with 4p 6= 1.
Abstract
In this paper, we investigate the following additive functional inequality kf(x) + f(y) + f(z) + f(w)k · kf(x + y) + f(z + (0.1) w)k in normed modules over a C¤-algebra. This is applied to understand homomor-phisms in C¤-algebras. Moreover, we prove the generalized Hyers-Ulam stability of the functional in- equality (0.2) kf(x) + f(y) + f(z) + f(w)k · kf(x + y + z + w)k + µjjxjjpjjyjjpjjzjjpjjwjjp in real Banach spaces, where µ; p are positive real numbers with 4p 6= 1.
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