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Convex Analysisの二,三の進展について

Fractional Differential Equations

Introduction to linear and nonlinear programming

Real and Complex Analysis

Tables of integrals

Preface Organization of the Book Notations I Convex Functions and Jensen's Inequality II Some Recent Results Involving Means III Bernoulli's Inequality IV Cauchy's and Related Inequalities V Hoelder and Minkowski Inequalities VI Generalized Hoelder and Minkowski Inequalities VII Connections Between General Inequalities VIII Some Determinantal and Matrix Inequalities IX Cebysev's Inequality X Gruss' 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 Inequations XVII The Centroid Method in Inequalities XVII Triangle Inequalities XVIII Norm Inequalities XIX More on Norm Inequalities XX Gram's Inequality XXI Frejer-Jackson's Inequalities and Related Results XXII Mathieu's Inequality XXIII Shannon's Inequality XXIV Turan's Inequality from the Power Sum Theory XXV Continued Fractions and Pade Approximation Method XXVI Quasilinearization Methods for Proving Inequalities XXVIII Dynamic Programming and Functional Equation Approaches to Inequalities XXIX Interpolation Inequalities XXX Minimax Inequalities Name Index

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Classical and New Inequalities in Analysis

Convex Functions. Jensen's and Jensen-Steffensen's Inequalities. Reversals, Refinements, and Converses of Jensen's and Jensen-Steffensen's Inequalities. Applications of Jensen's Inequality to Means and H*adolder's Inequalities. Hermite-Hadamard's and Jensen-Petrovi*aac's Inequalities. Popoviciu's, Burkill's, and Steffensen's Inequalities. *ajCeby*ajsev-Gr*aduss', Favard's, Berwald's, Gauss-Winckler's, and Related Inequalities. Hardy's, Hilbert's, Opial's, Young's, Nanson's, and Related Inequalities. General Linear Inequalities for Convex Sequences and Functions. Orderings and Convexity-Preserving Transformations. Convex Functions and Geometric Inequalities. Convexity, Majorization, and Schur-Convexity. Convexity and Log-Concavity Related Moment and Probability Inequalities. Muirhead's Theorem and Related Inequalities. Arrangement Ordering. Applications of Arrangement Ordering. Multivariate Arrangement Increasing Functions. References. Author Index. Subject Index.

Convex Functions, Partial Orderings, and Statistical Applications

I. Landau-Kolmogorov and related inequalities.- II. An inequality ascribed to Wirtinger and related results.- III. Opial's inequality.- IV. Hardy's, Carleman's and related inequalities.- V. Hilbert's and related inequalities.- VI. Inequalities of Lyapunov and of De la Vallee Poussin.- VII. Zmorovi?'s and related inequalities.- VIII. Carlson's and related inequalities.- IX. Inequalities involving kernels.- X. Convolution, rearrangement and related inequalities.- XI. Inequalities of Caplygin type.- XII. Inequalities of Gronwall type of a single variable.- XIII. Gronwall inequalities in higher dimension.- XIV. Gronwall inequalities on other spaces: discrete, functional and abstract.- XV. Integral inequalities involving functions with bounded derivatives.- XVI. Inequalities of Bernstein-Mordell type.- XVII. Methods of proofs for integral inequalities.- XVIII. Particular inequalities.- Name Index.

Inequalities Involving Functions and Their Integrals and Derivatives

A sharp Hadamard s inequality is proved for the class of functions introduced by Godunova and Levin A new class P I of quasi convex functions on an interval I is introduced f I R belongs to P I i for all x y I and f x y f x f y and a sharp Hadamard s inequality is proved for that class The results obtained can e g be applied for the class of nonnegative monotone functions and some applications are pointed out Introducton Let I a b be an interval on the real line let f I R be a convex function and let a b I a b We consider the well known Hadamard s inequality f a b b a Z b

Some inequalities of Hadamard type

In Chapter 1 a very brief and rapid review of some basic topics in Jensen's inequality for positive linear maps and Kantorovich inequality for several types are given. Some basic ideas and the viewpoints of the Mond-Peceric method are given. In Chapter 2 general converses of Jensen's inequality are considered. The Mond-Peceric method is used to obtain the bounds. Many interesting inequalities are particularly considered. In Chapter 3 a generalization of a theorem of Li-Mathias for the normalized positive linear maps as an application of the Mond-Peceric method is considered. Lower and upper bounds in converses of Jensen's type inequalities are given. The cases of the sharp inequalities are investigated. The conversions of Jensen's inequality and other inequalities are particularly considered. In Chapter 4 the previous results and the same methods are applied to obtain the inequalities for the means. Reverse inequalities of power operator means on positive linear maps are studied. Several properties of power operator means under the chaotic order are considered. New bounds in inequalities for power operator means are given. In chapter 5 the theory of operator means established by Kubo and Ando assocaiated with the operator monotone functions is introduced. Based on complementary inequalities to Jensen's inequalities on positive linear maps, complementary inequalities to Ando's inequalities assocaiated with operator means are studied. In Chapter 6 the results and the same methods in the chapter 2 are applied to obtain the inequalities for the Hadamard product. Then the reverses inequalities on the Hadamard product of operators and operator means are considered. General inequalities for the Hadamard product of operators are observed. In chapter 7 a brief survey of several applications of both Furuta inequality and generalized Furuta inequality is given. In Chapter 8 the claims preserving the operator order and the chaotic order are considered as an application of the Mond-Peceric method. The overall results on the functions which preserve the operator order and the chaotic order are particularly considered.

Josip Pečarić

Papers

Classical and New Inequalities in Analysis

Convex Functions, Partial Orderings, and Statistical Applications

Inequalities Involving Functions and Their Integrals and Derivatives

Some inequalities of Hadamard type

Mond-Pecaric Method in Operator Inequalities