Bounds for the normalised Jensen functional
نویسندگان
چکیده
منابع مشابه
Bounds for the Normalised Jensen Functional
New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen’s inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon’s inequality and the positivity of Kullback-Leibler divergence are obtained.
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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 ...
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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
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2006
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270004051x