Author | Mitrinoviฤ, Dragoslav S. author |
---|---|
Title | Analytic Inequalities [electronic resource] / by Dragoslav S. Mitrinoviฤ |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1970 |
Connect to | http://dx.doi.org/10.1007/978-3-642-99970-3 |
Descript | XII, 404 p. online resource |
1. Introduction -- 1.1 Real Number System -- 1.2 Complex Number System -- 1.3 Monotone Functions -- 1.4 Convex Functions -- 2. General Inequalities -- 2.1 Fundamental Inequalities -- 2.2 Abelโs Inequality -- 2.3 Jordanโs Inequality -- 2.4 Bernoulliโs Inequality and its Generalizations -- 2.5 ?ebyลกevโs and Related Inequalities -- 2.6 Cauchyโs and Related Inequalities -- 2.7 Youngโs Inequality -- 2.8 Hรถlderโs Inequality -- 2.9 Minkowskiโs and Related Inequalities -- 2.10 Inequalities of Aczรฉl, Popoviciu, Kurepa and Bellman -- 2.11 Schweitzerโs, Diaz-Metcalfโs, Rennieโs and Related Inequalities -- 2.12 An Inequality of Fan and Todd -- 2.13 Grรผssโ Inequality -- 2.14 Means -- 2.15 Symmetric Means and Functions -- 2.16 Steffensenโs and Related Inequalities -- 2.17 Schurโs Inequality -- 2.18 Turรกnโs Inequalities -- 2.19 Bensonโs Method -- 2.20 Recurrent Inequalities of Redheffer -- 2.21 Cyclic Inequalities -- 2.22 Inequalities Involving Derivatives -- 2.23 Integral Inequalities Involving Derivatives -- 2.24 Inequalities Connected with Majorization of Vectors -- 2.25 Inequalities for Vector Norms -- 2.26 Mills Ratio and Some Related Results -- 2.27 Stirlingโs Formula -- 3. Particular Inequalities -- 3.1 Inequalities Involving Functions of Discrete Variables -- 3.2 Inequalities Involving Algebraic Functions -- 3.3 Inequalities Involving Polynomials -- 3.4 Inequalities Involving Trigonometric Functions -- 3.5 Inequalities Involving Trigonometric Polynomials -- 3.6 Inequalities Involving Exponential, Logarithmic and Gamma Functions -- 3.7 Integral Inequalities -- 3.8 Inequalities in the Complex Domain -- 3.9 Miscellaneous Inequalities -- Name Index