Stability of a cubic functional equation in intuitionistic random normed spaces

Abstract

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.

Nonlinear -Fuzzy stability of cubic functional equations

“…We brief the proof because it is similar as the random case [47,27]. Putting y = 0 in (4.1), we have…”

“…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.…”

On nonlinear stability in various random normed spaces

“…Recently, the notation of intuitionistic random normed space introduced by Chang et al [19]. In this section, we shall adopt the usual terminology, notations, and conventions of the theory of intuitionistic random normed spaces as in [22], [31], [33], [34], [40], [41], [42].…”

“…Recently, Alsina [18], Chang, et al [19], Mirmostafaee et al [20], [21], Miheţ and Radu [22], Miheţ et al [23], [24], [25], [26], Baktash et al [27], Eshaghi et al [28], Saadati et al [29], [30] investigated the stability in the settings of fuzzy, probabilistic, and random normed spaces.…”

On the Stability of a General Mixed Additive-Cubic Functional Equation in Random Normed Spaces

“…Now, we give one example to illustrate the main results of Theorem 3.6. This example is a modification of the example of Zhang et al 34 .…”