One service mathematic; . , has Jcndcml the 'Et moi, . . ~ si j'avait su comment CD revcnir, human race. It has put COIDDlOJI SCIISC back je n'y scrais point allC.' whc:rc it belongs, on the topmost shell next Jules Verne to the dusty canister labc1lcd 'dilcardcd nOD- The series is divergent; tbcre(on: we may be sense'. Eric T. Bcll able to do something with it o. Hcavisidc Mathematics is a tool for thought. A highly necessary tooll in a world where both feedbaclt and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other paJts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . .'; 'One service logic has rendered com puter science . . .'; 'One service category theory has rendered mathematics . . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Inhaltsverzeichnis
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.
