Classical and New Inequalities in Analysis

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Zusammenfassung
Presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities.

Inhalt
I. Convex functions and Jensen's inequality.- II. Some recent results involving means.- III. Bernoulli's inequality.- IV. Cauchy's and related inequalities.- V. Hölder's and Minkowski's inequalities.- VI. Generalized Hölder and Minkowski inequalities.- VII. Connections between general inequalities.- VIII. Some Determinantal and Matrix inequalities.- IX. ?ebyev's inequality.- X. Grüss' inequality.- XI. Steffensen's inequality.- XII. Abel's and related inequalities.- XIII. Some inequalities for monotone functions.- XIV. Young's inequality.- XV. Bessel's inequality.- XVI. Cyclic inequalities.- XVII. Triangle inequalities.- XVIII. Norm inequalities.- XIX. More on norm inequalities.- XX. Gram's inequality.- XXI. Fejér-Jackson's inequalities and related results.- XXII. Mathieu's inequality.- XXIII. Shannon's inequality.- XXIV. Turán's inequality from the power sum theory.- XXV. Continued fractions and Padé approximation method.- XXVI. Quasilinearizai ion methods for proving inequalities.- XXVII. The centroid method in inequalities.- XXVIII. Dynamic programming and functional equation approaches to inequalities.- XXIX. Interpolation inequalities.- XXX. Convex Mini max inequalities-equalities.- Name Index.

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