We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers–Ulam stability of the orthogonal Cauchy functional equation of Pexider type f 1 (x + y) = f 2 (x) + f 3 (y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz.

We determine some stability results concerning the pexiderized quadratic functional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of L-fuzzy normed spaces. AMS Mathematics Subject Classification (2010): 00A11; Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

In this paper, we prove the Ulam stability of Fréchet functional equation f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) arising from characterization inner product spaces and determine its best constant. Using result, give a result for pexiderized version equation.

The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy version. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...