Inequalities II

Cover
Title page
LIST OF CONTRIBUTORS
PREFACE
CONTENTS OF VOLUME I ("Inequalities")
Some Integral Inequalities - N. Aronszajn
Introduction
I. Application of the First Method
II. Application of the Second Method
III. Application to Harmonic Functions
IV. Applications to the Theory of Potentials
V. Final Remarks and Problems
References
Meromorphic Plane Maps Viewed from Space - E. F. Beckenbach
1. Introduction
2. The Distance Function
3. Notation
4. Jensen's Formula
5. The First Fundamental Theorem
6. The Spherical Characteristic
7. Convexity Properties
8. The Second Fundamental Theorem
References
A Metric Space Connected with Generalized Means - G. T. Cargo and O. Shisha
1. Introduction
2. Separability of the Metric Space of Equivalence Classes
3. The Metric Space of Canonical Functions
4. Determination and Estimation of Distances
5. Some Further Remarks
6. Simultaneous Reduction of Generalized Means
References
Asymptotic Cones and Duality of Linear Relations - Ky Fan
1. Introduction
2. Existence Theorems
3. Dual Extremal Problems
References
On the Inequality ||f'||² <= 4||f||||f"|| - Robert R. Kallman and Gian-Carlo Rota
1. Introduction and Main Result
2. The Inequality for Semi-Groups
3. LZ Spaces
4. Main Inequality
References
Metric Inequalities and Symmetric Differences - John B. Kelly
1. Introduction
2. Preliminaries
3. The Main Theorem
4. Normed Lattices
5. Inner Product Spaces
6. Normed Linear Spaces
7. Hausdorff Metrics
8. Ultrametric Spaces
9. Cases of Equality
10. Trigonometric Inequalities
References
Dependence of Some Classical Inequalities on the Index Set - H. W. McLaughlin and F. T. Metcalf
1. Introduction
2. Illustrations
3. Survey of Recent Results
4. Statements of Recent Results
5. Concluding Remark
References
Inequalities for Submatrices - Marvin Marcus
1. Statements of Inequalities
2. Derivations on Symmetry Classes
3. Proofs of Inequalities
References
Difference and Ratio Inequalities in Hilbert Space - B. Mond and O. Shisha
References
The Real Solution Set of a System of Algebraic Inequalities is the Projection of a Hypersurface in One More Dimension - T. S. Motzkin
References
Singularities of the n-Body Problem. II - Harry Pollard and Donald G. Saari
1. Introduction
2. Singularities and Collisions
3. The von Zeipel Conjecture
References
Integral Inequalities with Boundary Terms - Ray Redheffer
1. Purpose of This Paper
2. Notation
3. Lemmas Pertaining to the Nonsingular Case
4. Inequalities of Hardy-Littlewood Type
5. Inequalities of Weyl Type
6. Inequalities of Hlawka Type
7. Inequalities of Rayleigh Type
8. A Theorem of Sturmian Type
9. Inequalities of Block Type
10. Isolated Singularities
11. Another Method
References
Perturbation of Zeros of Analytic Functions. I - Paul C. Rosenbloom
1. Introduction
2. Perturbation Outside of a Weak Neighborhood of Zero
Appendix
References
Perturbation of Zeros of Analytic Functions. II - Paul C. Rosenbloom
I. Introduction
II. Perturbation of Simple Zeros
III. Perturbation of Multiple Zeros
IV. Generalization of the Weierstrass Preparation Theorem
Appendix
V. Some Other Criteria for Location of a Zero
References
Cardinal Interpolation and Spline Functions - I. J. Schoenberg
Introduction
I. A Few Properties of Spline Functions with Equidistant Knots
II. The Spaces L_p^m and L_[1]^m
III. The Space L₂^m
References
On Two Complementary Variational Characterizations of Eigenvalues - William Stenger
1. Introduction
2. Definitions
3. The Inequalities of Weyl
4. The Inequalities of Poincaré
5. A Unification of the Maximum-Minimum and the Minimum-Maximum Principles
6. Inequalities Derived from Variational Principles
References
Positive-Definite Matrices and Their Role in the Study of the Characteristic Roots of General Matrices - Olga Taussky
1. Introduction
2. Products of Two Positive-Definite Matrices
3. Products of Three Positive-Definite Matrices
4. The Cone of Positive-Definite Real Matrices and Trace AS with S Positive-Definite and A a Stable Matrix
5. Matrix-Valued Functions on the Space of Hermitian Matrices with Positive Values for Some Positive Arguments
6. The Range of AX + XA* with X Positive-Definite for A a Stable Matrix
References
Inequalities Expressing Degree of Convergence of Rational Functions - J. L. Walsh
References
Inequalities for Generalized Convex Functions - Zvi Ziegler
I. Introduction
II. Characterization of the Dual Cones and Applications
III. Sums of Generalized Convexity Cones and of Their Duals
IV. Generalized Absolutely Monotone Functions
References
On Certain Lemmas of Marcinkiewicz and Carleson - A. Zygmund
References
INDEX