[PDF] Top 20 Intuitionistic Fuzzy Stability of n-Dimensional Cubic Functional Equation: Direct and Fixed Point Methods

... Definition 3.1.4. An IFN-space ( , X P µ ν , , ) T is said to be complete if every Cauchy sequence in X is convergent to a point x ∈ X .For further details about IFN space one can see ([4, 7, 8, 12, 13, 16–20, 24, ... See full document

... Dhombres, Functional Equations in Several Variables, Cambridge Univ, Press, ...the stability of the linear transformation in Banach spaces, ...and Intuitionistic Fuzzy Stability of ... See full document

... of functional equations like’s additive, quadratic, cubic, quartic, mixed type functional equations in-solving only these types of functional equations were ...famous functional ... See full document

... The Hyers-Ulam stability theorem for the quadratic functional equation (1.1) was proved by F.skof for the functions f E : 1  E 2 where E 1 is the normed space and E 2 be a Banach space, the result ... See full document

... Generalized Fuzzy Normed Spaces, International Mathematical Forum, 4, 2009, ...the stability of the linear functional equation, ...Rassias, Stability of functional equations in ... See full document

... The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [3, 7, 8, 9, 10, 30, 20, ... See full document

... Hyers-Ulam-Rassias stability of functional equations. Since then, several stability problems for various func- tional equations have been investigated in [, , , –, , ...quadratic ... See full document

... to point out the direct method for studying the stability of func- tional ...the fixed point alternative method to solve the Ulam ...the fixed point alternative method to ... See full document

... two methods is successfully extended to obtain a fuzzy approximate solutions to functional equations 14, ...the direct method and fixed alternative method for functional ... See full document

... the fixed-point method to the investigation of the Jensen functional equation see 12, 13 for the first ...using fixed point methods, the stability problems of ... See full document

... Over the last seven decades, the above problem was tackled by numerous authors and its solutions via various forms of functional equations including mixed type additive and cubic functional equations ... See full document

... This stability phenomenon is called generalized Hyers-Ulam stability and has been extensively investigated for different functional ...lim n→∞ 2 1 n f (2 n x), if p < 1; and ... See full document

... The stability concept that was introduced by Rassias’ theorem provided a large influence to a number of mathematicians to develop the notion of what is known today with the term Hyers-Ulam-Rassias stability ... See full document

... In 1940, Ulam gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. The first stability problem concerning group homomorphisms was raised by ... See full document

... of stability problems for functional equations is related to a question of Ulam [1] concerning the stability of group homomorphisms and it was affirmatively answered for Banach spaces by Hyers ... See full document

... f (x + y) + f (x − y) = 2f(x) + 2f (y) (1.1) is related to a symmetric bi-additive function [30, 31]. It is natural that this equa- tion is called a quadratic functional equation. In particular, every ... See full document

... a fixed point method was proposed, by showing that many theorems concerning the stability of Cauchy, Jensen, quadratic, cubic, quartic, and monomial functional equations are ... See full document

... The stability of mixed type functional equations have been extensively investigated by a number of math- ematicians in referenes (see [3–5, 14–22, 28–31, 33–38, 43, 48, ...the fixed point ... See full document

... (3.41) for all x, y, z, w ∈ U, t > 0 and α > 0. By letting n → ∞ in (3.41), we find that ν ∆c(x,y,z,w) ( t ) = 1 for all t > 0, which implies ∆c ( x, y, z, w ) = 0 and so c satisfies (1.9) for all x, y, ... See full document

... the stability of the linear functional ...the stability of the linear transformation in Banach ...the stability of the linear mapping in Banach ...S: Functional Equations and ... See full document