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Abstract
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.
Highlights
The theory of random normed spaces is important as a generalization of deterministic result of normed spaces and in the study of random operator equations
We present the Hyers-Ulam stability of Cubic functional equation i=1 i=1 f ixi + jx j + kxk n
From the Theorem 5.1, we obtain the following Corollary concerning the stability for the functional equation (1.4)
Summary
The theory of random normed spaces (briefly, RN-Spaces) is important as a generalization of deterministic result of normed spaces and in the study of random operator equations. The notion of an RN-Space corresponds to the situations when we do not know exactly the norm of the point and we know only probabilities of possible values of this norm. Random Theory has many applications in several fields, for example, population dynamics, computer programming, nonlinear dynamical system, nonlinear operators, statistical convergence and so forth. They established the general solution and the generalized Hyers-Ulam stability for the functional equation. The solution and stability of the succeeding cubic functional equation, f ( x + ky) − kf ( x + y) + kf ( x − y) − f (x − ky) = 2k (k 2 −1) f ( y) (1.2). The authors investigate the general solution and generalized Hyers-Ulam stability of a new type of n-dimensional cubic functional equation i=0 i i j k i j (1.4). Where n is greater than or equal to 4, in Random Normed Space by using direct and fixed-point method
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