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We take into account the stability of ring homomorphism and ring derivation in intuitionistic fuzzy Banach algebra associated with the Jensen functional equation. In addition, we deal with the superstability of functional equationf(xy)=xf(y)+f(x)yin an intuitionistic fuzzy normed algebra with unit.

Abstract. In this article, we prove the generalized Hyers-Ulam stability of the following Cauchy additive functional equationin fuzzy Banach spaces for any fixed nonzero integer n .Mathematics subject classification (2010): 39B52, 46S40.

We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.