Stability of pexider equations on semigroup with no neutral element

Let s be a commutative semigroup with no neutral element,y a banach space,and ℂ the set of complex numbers. in this paper we prove the hyers-ulam stability for pexider equation ∥f x + y - g x - h (y) ∥ ≤ ε for all x,y ∈ s,where f,g,h: s → y. using jung's theorem we obtain a better bound than that usually obtained. also,generalizing the result of baker (1980) we prove the superstability for pexider-exponential equation f t + s - g t h (s) ≤ ε for all t,s ∈ s,where f,g,h: s → ℂ. as a direct consequence of the result we also obtain the general solutions of the pexider-exponential equation f t + s = g t h (s) for all t,s ∈ s,a closed form of which is not yet known. © 2014 jaeyoung chung.