Approximate functional inequalities by additive mappings
نویسندگان
چکیده
منابع مشابه
Functional Inequalities Associated with Additive Mappings
The functional inequality ‖f x 2f y 2f z ‖ ≤ ‖2f x/2 y z ‖ φ x, y, z x, y, z ∈ G is investigated, where G is a group divisible by 2, f : G→ X and φ : G3 → 0,∞ are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with 1 φ 2x,−x, 0 0 φ 0, x,−x x ∈ G and 2 limn→∞ 1/2 φ 2 1x, 2y, 2z 0, or limn→∞2φ x/2n−1, y/2, z/2 0 x, y, z ∈ G , imply that ...
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In 1940, Ulam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G′ with metric ρ(·,·). Given > 0, does there exist a δ > 0 such that if f :G→G′ satisfies ρ( f (xy), f (x) f (y)) < δ for all x, y ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2012
ISSN: 1846-579X
DOI: 10.7153/jmi-06-43