On the stability of a cubic functional equation in random 2-normed spaces

Abstract

In this article, we propose to determine some stability results for the functional equation of cubic in random 2-normed spaces which seems to be a quite new and interesting idea. Also, we define the notion of continuity, approximately and conditional cubic mapping in random 2-normed spaces and prove some interesting results.

Complete quenching phenomenon for a parabolic p-Laplacian equation with a weighted absorption

“…We refer to [32, 35, 44, 45] for the nonlinear absorption and source, nonlinear gradient absorption or source, and [9, 10, 22] for singular absorptions. Also, we refer to [46, 47] for the semilinear equations with an exponential source. When , equation (1.1) is known as a limit model of a class of problems arising in Chemical Engineering corresponding to enzymatic kinetics and hetergeneous catalyst of Langmuir–Hinshelwood type, see [3, 9, 12, 15, 22, 39, 43] and references therein.…”

Stability of a generalized quadratic functional equation in intuitionistic fuzzy 2-normed space

“…Recently, considerable attention has been increasing to the problem of fuzzy stability of functional equations. Several various fuzzy stability results concerning Cauchy, Jensen, simple quadratic, and cubic functional equations have been investigated [1,6,11,23,31] Quite recently, the stability results in the setting of intuitionistic fuzzy normed space were studied in [7,[18][19][20]22]respectively, while the idea of intuitionistic fuzzy normed space was introduced in [25].…”

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

“…Quite recently, Chang [5] has established the stability of higher ring derivation in intuitionistic fuzzy Banach algebras associated to the Jensen type functional equation. In the recent past, Alotaibi and Mohiuddine [2] established the Ulam stability of a cubic functional equation in random 2-normed spaces, while the notion of random 2-normed spaces was introduced by Goleţ [8] and further studied in [18,26,21]. Now, we recall some notations and basic definitions which will be used throughout the paper.…”