On the Ulam Stability of Cauchy Functional Equation in IFN-Spaces

Abstract

Abstract:The aim of this paper is to establish some stability results concerning the Cauchy functional equation f (x + y) = f (x) + f (y) in the framework of intuitionistic fuzzy normed spaces.

Stability of Pexiderized Quadratic Functional Equation in Random 2-Normed Spaces

“…Some important Ulam stability problems on Cauchy equation on semigroups, approximately additive mappings, and Jensen equation have been investigated by Gajda [10], Gȃvruta [11], and Jung [12], respectively. Until now, the stability problems for different types of functional equations in various spaces have been extensively studied, for instance, by Mirmostafaee and Moslehian [13,14], Rassias [15], Chang et al [16,17], Xu et al [18], Jun and Kim [19], Mursaleen et al [20][21][22], and many others. Also very interesting results on additive, quadratic, and cubic functional equations have been achieved by Mohiuddine et al [23][24][25][26][27][28][29].…”

On the stability of some positive linear operators from approximation theory

“…A new type of stability for functional equations was introduced by Aoki [6] and Rassias [7] by replacing ε in the Hyers theorem with a function depending on x and y, such that the Cauchy difference can be unbounded. For other results on the Hyers-Ulam stability of functional equations one can refer to [2,8,9]. The Hyers-Ulam stability of linear operators was considered for the first time in the papers by Miura, Takahasi et al (see [10][11][12]).…”