Abstract
We investigate the generalized Hyers-Ulam stability of the functional inequalities∥f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)∥≤∥2f(x)∥and∥f((y−x)/3)+f((x−3z)/3)+f((3x+3z−y)/3)∥≤∥f(x)∥in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.
Highlights
Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems
We investigate the generalized Hyers-Ulam stability of the functional inequalities f x y z /4 f 3x−y−4z /4 f 4x 3z /4 ≤ 2f x and f y−x /3 f x−3z /3 f 3x 3z−y /3 ≤ f x in non-Archimedean normed spaces in the spirit of the Th
Among these was the following question concerning the stability of homomorphisms
Summary
Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. A function · : X → R is a non-Archimedean norm valuation if it satisfies the following conditions: i x 0 if and only if x 0; ii rx |r| x r ∈ K, x ∈ X ; iii the strong triangle inequality ultrametric , namely, x y ≤ max x , y x, y ∈ X . Gilanyi 23 and Fechner 25 proved the generalized Hyers-Ulam stability of the functional inequality 1.3 .
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