A Fixed Point Approach to Approximate Bi-Homomorphisms and Bi-Derivations in Intuitionistic Fuzzy Normed Spaces

Javad Shokri, Sajad Abdollahnajad, Mohammad Ali Abolfathi

Abstract

In this paper, we define bi-homomorphisms and bi-derivation in intuitionistic fuzzy normed spaces (IFNspaces). The fixed point methods are implemented to generalized Hyers-Ulam stability of bi-homomorphisms and biderivations associated to the following 2-dimensional vector variable quadratic functional equation in intuitionistic fuzzy normed spaces
f (x + y, z + w) + f (x -  y, z -  w) = 2f (x, z) + 2f (y, w),
where f (x, 0) = f (0, y) = 0 for all x, y \in X.