Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings

Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings

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 ...

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

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 ...

Extended Stability Problem for Alternative Cauchy–jensen Mappings

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings.