Stability Of Cubic Functional Equation Research Articles

Hyers-Ulam-Rassias stability of cubic functional equations in fuzzy normed spaces

<abstract> <p>In this paper, two cubic functional equations are shown to be equivalent, Hyers-Ulam-Rassias stability of them is proved under some suitable conditions by the fixed point method in fuzzy normed spaces. Moreover, the fuzzy continuity of the solution of the functional equation is discussed.</p> </abstract>

Stability of Cubic Functional Equation in Random Normed Space

In this paper, we present the Hyers-Ulam stability of Cubic functional equation.
 
 where n is greater than or equal to 4, in Random Normed Space.

The stability of cubic functional equations in 2-Banach space

The stability of cubic functional equations in 2-Banach space

Nonlinear -Fuzzy stability of cubic functional equations

We establish some stability results for the cubic functional equations 3 f x + 3 y + f 3 x - y = 15 f x + y + 15 f x - y + 8 0 f y , f 2 x + y + f 2 x - y = 2 f x + y + 2 f x - y + 12 f x and f 3 x + y + f 3 x - y = 3 f x + y + 3 f x - y + 48 f x in the setting of various -fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First, we shall prove the stability of cubic functional equations in the -fuzzy normed space under arbitrary t-norm which generalizes previous studies. Then, we prove the stability of cubic functional equations in the non-Archimedean -fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis.Mathematics Subject Classification (2000): Primary 54E40; Secondary 39B82, 46S50, 46S40.

Hyers-Ulam Stability of Cubic Mappings in Non-Archimedean Normed Spaces

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x y) = 2f(x + y) + 2f(x y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non- Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

Stability of Cubic Functional Equation in the Spaces of Generalized Functions

We reformulate the following additive functional equation with n-independent variables as the equation for the spaces of generalized functions. Making use of the fundamental solution of the heat equation we solve the general solutions and the stability problems of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the regularizing functions, we extend these results to the space of distributions. 2000 MSC: 39B82; 46F05.