Handbook of Functional Equations

Handbook of Functional Equations

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As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), a€œThere are three reasons for the study of inequalities: practical, theoretical, and aesthetic.a€ On the aesthetic aspects, he said, a€œAs has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.a€ The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardya€“Hilbert and the Gabriel inequality, generalized Hardya€“Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemanna€“Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasza€“Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fishera€™s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.Recall now the known relation of the Shannon entropy of a normally distributed random variable Z ~ V(u, X), i.e. H(Z) ... difference between these entropies of uniform and Laplace is independent of the same scale matrix X, i.e. H3(X+ce) a€” H3(X 1) = p + # log p! ... Theorem 16 The generalized Fishera#39;s information J, of an ry.


Title:Handbook of Functional Equations
Author: Themistocles M. Rassias
Publisher:Springer - 2014-11-18
ISBN-13:

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