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
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