Asymptotic stability of the Cauchy and Jensen functional equations

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

Asymptotic behavior of alternative Jensen and Jensen type functional equations

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...

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

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 ...

Stability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors