Inequalities III

Title page LIST OF CONTRIBUTORS PREFACE CONTENTS OF PREVIOUS VOLUMES An Inequality and Associated Maximization Technique in Statistical Estimation for Probabilistic Functions of Markov Processes - Leonard E. Baum References Convexity, Hardy's Theorem, and the Lemma of Schwarz - E. F. Beckenbach 1. Introduction 2. Mean Values 3. The Integrand 4. The Measure Function 5. Hardy's Theorem 6. The Lemma of Schwarz 7. Applications 8. Convexity References Complex Linear Inequalities - Adi Ben-Israel 1. Introduction 2. Notation 3. Convex Cones and Duals 4. Linear Equations over Closed Convex Cones: Solvability Theorems 5. Homogeneous Linear Equations over Closed Convex Cones: Nontrivial Solutions 6. Applications to Inequalities Involving Matrices and Eigenvalues 7. Complex Programming References An Elementary, Unified Treatment of Complementary Inequalities - G. T. Cargo 1. Introduction 2. The Vertex Phenomenon 3. A General Class of Complementary Inequalities 4. Some Applications 5. Some Additional Results 6. Maximal Cases 7. Conclusion Addendum References A Comparison of Two Uniqueness Theorems for the Ordinary Differentiai Equation y'=f(x, y) - J. B. Diaz References Applications of the Cauchy-Schwarz Inequality to Some Extremal Problems - M. L. Eaton and l. Olkin 1. Introduction 2. An Extremal Problem 3. An Extension 4. A Problem of Chernoff and Savage Appendix References Extremal and Acute Bijections between Finite Point Sets - Jack Edmonds and Oved Shisha References Generalizations of the Cauchy-Schwarz and Hölder Inequalities - C. J. Eliezer and B. Mond 1. Introduction 2. Generalizations of Cauchy's Inequality 3. Generalizations of Hölder's Inequality References A Minimax Inequality and Applications - Ky Fan 1. A Minimax Inequality 2. A Geometric Formulation of the Minimax Inequality 3. Fixed Point Theorems 4. Sets with Convex Sections 5. Application in Potential Theory References Antieigenvalue Inequalities in Operator Theory - Karl Gustafson 1. Antieigenvalues 2. Initial-Value Problems References Nonreflexivity and the Girth of Spheres - R. E. Harrell and L. A. Karlovitz 1. Introduction 2. Girths and Nonreflexivity References Bounds for Deformations in Terms of Average Strains - Fritz John 1. Introduction 2. The Basic Identity Appendix. Inequalities for Functions of Bounded Mean Oscillation References A Further Generalization of Kirszbraun's Theorem - S. Karamardian References Hypermetric Spaces and Metric Transforms - John B. Kelly 1. Introduction and Principal Results 2. Concave Functions 3. A Combinatorial Lemma 4. Proof of Theorem 1 5. Proof of Theorem 2 References How Good Is the Simplex Algorithm? - Victor Klee and George J. Minty 1. Introduction 2. Preliminaries 3. Statement of Main Results 4. Proof That H(d+1,n+2) > 2H(d,n)+1 5. Proof That H(d+2,n+k+1) > kH(d,n)+k-1 6. Proof That α_d n^{[d/2]} < H(d,n) < β_d^{n[d/2]} 7. Replacement of H by Θ_s in the Inequalities of Previous Sections 8. Final Comments References A Generalization of the Class of Completely Convex Functions - D. Leeming and A. Sharma 1. Introduction 2. Preliminaries and Statement of Main Results 3. Properties of Fundamental Polynomials of the (p,L) Series 4. A Boundary-Value Problem 5. Estimates on the Fundamental Polynomials 6. Estimates for Completely W 2)-Convex Functions 7. (p, L) Series and Completely W2)-Convex Functions 8. Minimal Completely W_p-Convex Functions 9. Representation of Functions by (p,L) Series References Monotone Approximation - G. G. Lorentz 1. Introduction 2. Characterization of Polynomials of Best Approximation 3. Uniqueness of Polynomials of Best Approximation 4. Estimation of E_n^*(f) from Above 5. A New Result 6. Estimation of the Degree of Approximation from Below References A Dimension Inequality for Multilinear Functions - Marvin Marcus 1. Introduction 2. Proofs Convexity Preserving Scale Transformations - Albert W. Marshall and Frank Proschan 1. Introduction 2. Convex, Star-Shaped, and Superadditive Functions 3. Extensions to Other Domains 4. Logarithmic Convexity and Concavity References On Transposition Theorems in Complex Space - Bertram Mond 1. Introduction 2. Notation and a Preliminary Result 3. Results in Complex Space 4. Special Cases References The Differentiability of Weak Solutions of Elliptic Systems - Charles B. Morrey, Jr References Disadherents and Unisolvence - Theodore S. Motzkin 1. Introduction 2. Disadherents for Subfamilies of Various Universal Classes 3. Unisolvent Families of Plane Curves and Their Disadherents adherents and Nondisadherents References Variational Principles for Wave Equations, 1 - Paul C. Rosenbloom 1. Introduction 2. Variational Principles Associated with von Neumann's Theorem References Conformai Mapping of Nearly Circular Domains and Loewner's Differential Equation - Paul C. Rosenbloom 1. Introduction 2. Preliminary Remarks 3. Proof of the Preliminary Inequalities 4. Proof of Theorem 1 5. The Univalent Case References Inequalities in the Theory of Univalent Functions - Menahem Schiffer 1. Introduction 2. Coefficients of Univalent Functions 3. Grunsky Inequalities References Duality in Linear Range-Domain Implications - Johann Schröder 1. Introduction 2. Primal and Dual Properties 3. A Duality Theorem for Polyhedral Sets 4. The Special Case of Inverse Positivity 5. An Example 6. Generalizations References A Two Independent Variable Gronwall-Type Inequality - Donald R. Snow 1. Introduction 2. Main Theorem and Corollaries 3. Applications References Automorphs of Quadratic Forms as Positive Operators - Olga Taussky 1. Introduction 2. The Matrix of the Automorph Operator 3. The Case of Real T's 4. The Case of Positive T's 5. Which Real Characteristic Vectors of I Are Positive Definite, Which Positive Semidefinite, Which Indefinite? 6. The Adjoint Operator of I References Hardy-Littlewood Estimates for HP Functions - G. D. Taylor 1. Introduction 2. Main Results References Positive Cones in Hilbert Space and a Maximal Inequality - Benjamin Weiss References AUTHOR INDEX SUB]ECT INDEX