Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces

Abstract

Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) ε X × X : ∥ x∥ + ∥y∥ ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and taking values in Y. We consider also the Pexiderized Cauchy functional equation. © 2011 Najati et al.