the main goal of this paper is the study of the generalized hyers-ulam stability of the following functionalequation f (2x  y)  f (2x  y)  (n 1)(n  2)(n  3) f ( y)  2n2 f (x  y)  f (x  y)  6 f (x) where n  1,2,3,4 , in non–archimedean spaces, by using direct and fixed point methods.

In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

and Applied Analysis 3 The functional equation 1.7 was first solved by Kannappan. In fact he proved that a mapping f on a real vector space is a solution of 1.7 if and only if there exists a symmetric biadditive mapping B and an additive mapping A such that f x B x, x A x , for any x see 9 . The stability problem for 1.7 is also studied in 26 . Moreover 1.7 was pexiderized and solved by Kannapp...

We will establish stability of Fréchet functional equation

In this paper, we solve the additive ρ -functional inequalities ‖ f (x+ y)− f (x)− f (y)‖ ∥∥∥ρ ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ (0.1) and ∥∥∥2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ ‖ρ ( f (x+ y)− f (x)− f (y))‖ , (0.2) where ρ is a fixed non-Archimedean number with |ρ| < 1 . Furthermore, we prove the Hyers-Ulam stability of the additive ρ -functional inequalities (0.1) and (0.2) in non-Archimedean...

and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...