ScienceAsia - Journal of The Science Society of Thailand

ABSTRACT: We studied the stability of the alternative functional equation ?f (x ? y) ? 2f (x) + f (x + y)? ? f (x ? y) + f (x + y)? = 0 (*) for all x, y ? G, where f : G ? B is a function from commutative group G to a real Banach space B, and found that if ?f (x ? y) ? 2f (x) + f (x + y)? ? ? or ?f (x ? y) + f (x + y)? ? ? for each x, y ? G, then there exists a solution f ? : G ? B of (*) such that ?f (x) ? f ? (x)? ? 12?. The general solution of (*) was also achieved.

A complementary Hyers-Ulam stability of alternative equation of Jensen type

Teerapol Sukhonwimolmal