As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), "There are three reasons for the study of inequalities: practical, theoretical, and aesthetic." On the aesthetic aspects, he said, "As 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."

The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy-Hilbert and the Gabriel inequality, generalized Hardy-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 Riemann-Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz-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 Fisher's information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Inhalt

On a Relation Between the HardyHilbert and the Gabriel Inequality (V. Adiyasunen, T. Batbold).- Mathematical Models of Mechanical Fields in Media with Inclusions and Holes (M. Bryla, A.V. Krupoderov, A.A. Kushunin, V. Mityushev).- A Note on the Functions that are Approximately p-Write Affine (J. Brzdek).- Multiplicative Ostrowski and Trapezoid Inequalities (P. Cerone, S. Dragomir, E. Kikianty).- A Survey on Ostrowski Type Inequalities for RiemannStieltjes Integral (W.S. Cheung, S.S. Dragomir).- Invariance in the Family of Weighted Gini Means (I. Costin, G. Toader).- Functional Inequalities and Analysis of Contagion in the Financial Networks (P. Daniele, S. Giuffe,k M. Lorino, A. Maugeri, C. Mirabella).- Comparisons of Means and Related Functional Inequalities (W. Fechner).- Constructions and Extensions of Free and Controlled Additive Relations (T. Glavosits, A. Szaz).- Extremal Problems in Polynomials and Entire Functions (N.K. Govil, Q. M. Tariq).- On Approximation Properties of SzaszMirakyan Operators (V. Gupta).- Generalized HardyHilbert Type Inequalities on Multiple Weighted Orlicz Spaces (K. Jichang).- Inequalities for the Fisher's Information Measures (C.P. Kitsos, T.L. Toulias).- Applications of Functional Equations to Dirichlet Problem for Double Connected Domains (V. Mityushev).- Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters (D. Motreanu, V.V. Motreanu).- On Strongly Convex Functions and Related Classes of Functions (K. Nikodem).- Some New Algorithms for Solving General Equilibrium Problems (M.A. Noor, Th.M. Rassias).- Contractive Operators in Relational Metric Spaces (M. Turinici).- Half-Discrete Hilbert-Type Inequalities, Operators, and Compositions (B. Yang).- Some Results Concerning Hardy and Hardy-Type Inequalities (N.B. Zographopoulos).