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A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation. (English) Zbl 0957.39008

Let V be a normed vector space and X a Banach space, and let f,g,h:VX. The authors prove that the Pexider equation

f(x+y)=g(x)+h(y)

is stable in the following sense: If there exists a real number p1, such that

f ( x + y ) - g ( x ) - h ( y )x p +y p

for all x,yV{0}, then there exists exactly one additive map T:VX such that

f ( x ) - T ( x ) - f ( 0 )C(p)x p

for all xV. Here C(p) is a certain specified constant.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges