Titlebook: General Inequalities 3; 3rd International Co E. F. Beckenbach,Wolfgang Walter Book 1983 Springer Basel AG 1983 applied mathematics.inequali

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On an Algorithmic Method to Prove InequalitiesIn this paper, we give a summary of a new method for proving inequalities. For the sake of brevity, we omit the full proofs of the main theorems; however, we do give their principal ideas, along with a number of applications. For details, the reader is referred to [2], [3].

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螢火蟲

Easy Proofs of Hard InequalitiesMany inequalities are difficult to discover but easy to prove, just as many proofs are difficult to motivate but easy to follow. Ignoring the problems of discovery and motivation, we give simple new proofs for a variety of important inequalities.

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Inequalities and Mathematical ProgrammingExtension of the Rado-Popoviciu inequalities, which in turn generalize the usual arithmetic-geometric inequality, are given here. These extensions are established by means of suitable equalities. Mathematical programming problems involving a monotonically increasing convex function are also examined.

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Bounds for the Greatest and the Least Characteristic Roots of a Positive Definite Matrix Using PowerIn an earlier paper [1], we showed how to get bounds for the greatest and the least characteristic roots of a positive definite matrix using some simple inequalities for the trace. Here we show how we can obtain improved results using powers of 2.

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Combinatorial Inequalities, Matrix Norms, and Generalized Numerical Radii. IITwo recently established combinatorial inequalities are used in order to investigate the submultiplicativity of a new family of norms on the algebra of n × n complex matrices. The family is that of the C-numerical radii, which are generalizations of the classical numerical radius.