Classical and New Inequalities in Analysis

This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, HAlder, Minkowski, Stefferson, Gram, FejA(c)r, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.

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. ?ebyšev’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.