## Mathematical InequalitiesThe book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics. * It contains a variety of inequalities which find numerous applications in various branches of mathematics. * It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books. * It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics. * Each chapter ends with some miscellaneous inequalities for futher study. * The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course. |

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absolutely continuous functions applying b a d Cl Cl concave function convex function convex set COROLLARY denote desired inequality differential equations discrete inequalities Dividing both sides Dragomir elementary inequality Equality holds established by Pachpatte Euclidean space Favard inequality finite following identities following inequality holds following theorem FP(x Fubini's theorem function f function on a,b given in Theorem gradu(x Hadamard Hadamard's inequality Hardy’s inequality Hölder's inequality independent variables inequalities established inequalities involving inequality given inequality with indices interval Jensen’s inequality KXEn Lemma Let f log-convex Lyapunov Math n-tuple nontrivial solution obtain Opial-type inequalities Opial’s inequality Peˇcari´c Pećarić Poincaré proof is complete proof of inequality proof of Theorem real numbers real-valued functions REMARK required inequality resulting inequality right-hand side satisfying Schwarz inequality smooth functions Suppose XX_1 Young's inequality zeros

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Page iv - A. Bjorner, RH Dijkgraaf, A. Dimca, AS Dow, JJ Duistermaat, E. Looijenga, JP May, I. Moerdijk, SM Mori, JP Palis, A. Schrijver, J.

Page ix - Polya in 1934 (see [ 2 ]), an enormous amount of effort has been devoted to the discovery of new types of inequalities, and to the application of inequalities in many parts of analysis.

Page 589 - GS Yang, On a certain result of Z. Opial, Proc. Japan Acad. 42 (1966), 78-83.

Page 7 - In the past several years there has been considerable interest in the application of differential and integral inequalities in many parts of analysis.

Page 577 - Distribution of the zeros of solutions of a linear differential equation, Soviet Math. Dokl. 5 (1964), 818-821. 121. A. Ju. Levin, Integral criteria for the equation x" + q(t)x = 0 to be non-oscillatory, Uspehi Mat.