Intuitionistic Fuzzy Stability of Jensen Type Mapping

Abstract

Abstract. In this paper we prove result for Jensen type mapping in the setting of intuitionistic fuzzy normed spaces. We generalize a Hyers-Ulam stability result in the framework of classical normed spaces.

Solution and two types of Ulam-Hyers stability of n􀀀 dimensional cubic-quartic functional equation in intuitionistic normed spaces

“…[43] A sequence {x n } in an IFN-space X, P µ,ν , T is called a Cauchy sequence if, for any ε > 0 and t > 0, there exists n 0 ∈ N such that…”

“…Further generalizations on the above stability results was given in [16,21,22,40]. Since then several stability problems for various functional equations have been investigated in [1, 3-13, 17, 25, 34, 37, 39, 47]; various fuzzy stability results concerning Cauchy, Jensen, quadratic and cubic functional equations were discussed in [19,20,[29][30][31][32][43][44][45]. Jun and Kim [26] considered the following functional equation It is easy to show that the function f (x) = x 4 satisfies the functional equation (1.2), which is called a quartic functional equation and every solution of the quartic functional equation is said to be a quartic function.…”

Solution and intuitionistic fuzzy stability of n- dimensional quadratic functional equation: direct and fixed point methods

“…Definition 3.9 [39] The sequence {x n } is said to be convergent to a point x ∈ X (denoted by x n Zhou [42] proved a stability property of the functional equation…”

Nonlinear -Fuzzy stability of cubic functional equations

“…Later a number of mathematicians worked on the stability of some types of cubic equations [4,[17][18][19]. Furthermore, Mirmostafaee and Moslehian [20], Mirmostafaee et al [21], Alsina [22], Miheţ and Radu [23] and others [24][25][26][27][28] investigated the stability in the settings of fuzzy, probabilistic, and random normed spaces.…”