General inequalities 2 : proceedings of the Second International Conference on General Inequalities, held in the Mathematical Research Institut at Oberwolfach, Black Forest, July 30-August 5, 1978

Front Matter....Pages i-xix Front Matter....Pages 1-1 Origin of the Mathematical Research Institute Oberwolfach at the Countryseat ‘Lorenzenhof’....Pages 3-13 Front Matter....Pages 15-15 A Functional Inequality Arising in Combinatorics....Pages 17-28 Pairs of Sums of Three Squares of Integers Whose Product Has the Same Property....Pages 29-36 Combinatorial Inequalities, Matrix Norms, and Generalized Numerical Radii....Pages 37-46 The Case n = 2 of the Goldberg-Straus Inequality....Pages 47-51 Front Matter....Pages 53-53 Inequalities Involving Infinite Matrices with Nonnegative Entries....Pages 55-80 On Pseudoconvex Quadratic Forms....Pages 81-88 Some Inequalities for Positive Definite Matrices....Pages 89-90 Inequalities Connecting Eigenvalues and Nonprincipal Subdeterminants....Pages 91-105 Front Matter....Pages 107-107 Minimum Properties of Eigenvalues — Elementary Proofs....Pages 109-120 Infinite Systems of First-Order Partial-Differential Functional Inequalities....Pages 121-126 Inequalities for Fourier-Stieltjes Transformations of Functions of Bounded Variation....Pages 127-133 Front Matter....Pages 135-135 ℓ 1 -Bounds for Inner Products....Pages 137-142 On the Location of the Intermediate Point in Taylor’s Theorem....Pages 143-144 On Hölder’s Inequality....Pages 145-150 On Some Integral Inequalities of E. T. Copson....Pages 151-159 On Enveloping Series for Some of the Special Functions, and on Integral Inequalities Involving Them....Pages 161-175 Front Matter....Pages 177-177 A Generalization of Theorems Concerning a Nonlinear Functional Inequality in a Single Variable....Pages 179-184 Generalized Subadditivity and Convexity....Pages 185-192 Homogeneity Sets for Jensen-Convex Functions....Pages 193-201 Front Matter....Pages 203-203 On an Interpolation Problem and Spline Functions....Pages 205-231 On Approximately Additive Mappings....Pages 233-251 Front Matter....Pages 253-253 New Versions of the Hahn-Banach Theorem....Pages 255-266 On Interpolation of Weak-Type Operators....Pages 267-275 A Generalized Schur-Hardy Inequality on Normed Köthe Spaces....Pages 277-286 Mean Values and Function Spaces....Pages 287-295 Front Matter....Pages 297-297 The Banach-Steinhaus Theorem with Rates, and Applications to Various Branches of Analysis....Pages 299-331 Harnack’s Inequalities for Operators....Pages 333-339 General Inequalities and Fixed-Point Problems....Pages 341-353 Front Matter....Pages 355-355 Eine Geometrische Ungleichung und Ihre Anwendung....Pages 357-366 A Sturm-Liouville Inequality with Applications to an Isoperimetric Inequality for Volume in Terms of Injectivity Radius, and to Wiedersehen Manifolds....Pages 367-377 The Formulas of Weierstrass and the Fundamental Theorem of Algebra for Minimal Surfaces....Pages 379-409 Some Inequalities for Univalent Functions with Quasiconformal Extensions....Pages 411-415 Front Matter....Pages 417-417 On a Family of Functional Inequalities....Pages 419-427 How to Derive all L P — Metrics from a Single Probabilistic Metric....Pages 429-434 On a Functional Inequality....Pages 435-440 General Solution of an Inequality Containing Several Unknown Functions, with Applications to the Generalized Problem of “How to Keep the Expert Honest”....Pages 441-445 Front Matter....Pages 447-447 Why Study Inequalities?....Pages 449-449 The n-TH Partial Sums of Jacobi Elliptic Functions....Pages 450-450 Problems in the Theory of Infinite Matrices....Pages 451-452 Front Matter....Pages 447-447 The Motion of a Simple Pendulum with Uniformly Shortening String Length....Pages 453-454 Remarks Concerning Extensions of the Gamma Function....Pages 455-457 A Problem on Normed Köthe Spaces....Pages 458-458 Remarks on a Generalization of the Schur-Hardy Inequality....Pages 459-460 A Note on the Foregoing Remarks of R. N. Mohapatra....Pages 461-461 A Problem in Univalent-Function Theory....Pages 462-462 On a Majorization of Distances between the Values of a Family of Functions and a Fixed Point....Pages 463-464 Area of a Triangle and the Product of Its Side Lengths....Pages 465-466 A Minimum Property of the Square....Pages 467-467 Back Matter....Pages 469-472 Front Matter....Pages i-xix Front Matter....Pages 1-1 Origin of the Mathematical Research Institute Oberwolfach at the Countryseat ‘Lorenzenhof’....Pages 3-13 Front Matter....Pages 15-15 A Functional Inequality Arising in Combinatorics....Pages 17-28 Pairs of Sums of Three Squares of Integers Whose Product Has the Same Property....Pages 29-36 Combinatorial Inequalities, Matrix Norms, and Generalized Numerical Radii....Pages 37-46 The Case n = 2 of the Goldberg-Straus Inequality....Pages 47-51 Front Matter....Pages 53-53 Inequalities Involving Infinite Matrices with Nonnegative Entries....Pages 55-80 On Pseudoconvex Quadratic Forms....Pages 81-88 Some Inequalities for Positive Definite Matrices....Pages 89-90 Inequalities Connecting Eigenvalues and Nonprincipal Subdeterminants....Pages 91-105 Front Matter....Pages 107-107 Minimum Properties of Eigenvalues — Elementary Proofs....Pages 109-120 Infinite Systems of First-Order Partial-Differential Functional Inequalities....Pages 121-126 Inequalities for Fourier-Stieltjes Transformations of Functions of Bounded Variation....Pages 127-133 Front Matter....Pages 135-135 l 1 -Bounds for Inner Products....Pages 137-142 On the Location of the Intermediate Point in Taylor’s Theorem....Pages 143-144 On Hölder’s Inequality....Pages 145-150 On Some Integral Inequalities of E. T. Copson....Pages 151-159 On Enveloping Series for Some of the Special Functions, and on Integral Inequalities Involving Them....Pages 161-175 Front Matter....Pages 177-177 A Generalization of Theorems Concerning a Nonlinear Functional Inequality in a Single Variable....Pages 179-184 Generalized Subadditivity and Convexity....Pages 185-192 Homogeneity Sets for Jensen-Convex Functions....Pages 193-201 Front Matter....Pages 203-203 On an Interpolation Problem and Spline Functions....Pages 205-231 On Approximately Additive Mappings....Pages 233-251 Front Matter....Pages 253-253 New Versions of the Hahn-Banach Theorem....Pages 255-266 On Interpolation of Weak-Type Operators....Pages 267-275 A Generalized Schur-Hardy Inequality on Normed Köthe Spaces....Pages 277-286 Mean Values and Function Spaces....Pages 287-295 Front Matter....Pages 297-297 The Banach-Steinhaus Theorem with Rates, and Applications to Various Branches of Analysis....Pages 299-331 Harnack’s Inequalities for Operators....Pages 333-339 General Inequalities and Fixed-Point Problems....Pages 341-353 Front Matter....Pages 355-355 Eine Geometrische Ungleichung und Ihre Anwendung....Pages 357-366 A Sturm-Liouville Inequality with Applications to an Isoperimetric Inequality for Volume in Terms of Injectivity Radius, and to Wiedersehen Manifolds....Pages 367-377 The Formulas of Weierstrass and the Fundamental Theorem of Algebra for Minimal Surfaces....Pages 379-409 Some Inequalities for Univalent Functions with Quasiconformal Extensions....Pages 411-415 Front Matter....Pages 417-417 On a Family of Functional Inequalities....Pages 419-427 How to Derive all L P — Metrics from a Single Probabilistic Metric....Pages 429-434 On a Functional Inequality....Pages 435-440 General Solution of an Inequality Containing Several Unknown Functions, with Applications to the Generalized Problem of “How to Keep the Expert Honest”....Pages 441-445 Front Matter....Pages 447-447 Why Study Inequalities?....Pages 449-449 The n-TH Partial Sums of Jacobi Elliptic Functions....Pages 450-450 Problems in the Theory of Infinite Matrices....Pages 451-452 Front Matter....Pages 447-447 The Motion of a Simple Pendulum with Uniformly Shortening String Length....Pages 453-454 Remarks Concerning Extensions of the Gamma Function....Pages 455-457 A Problem on Normed Köthe Spaces....Pages 458-458 Remarks on a Generalization of the Schur-Hardy Inequality....Pages 459-460 A Note on the Foregoing Remarks of R. N. Mohapatra....Pages 461-461 A Problem in Univalent-Function Theory....Pages 462-462 On a Majorization of Distances between the Values of a Family of Functions and a Fixed Point....Pages 463-464 Area of a Triangle and the Product of Its Side Lengths....Pages 465-466 A Minimum Property of the Square....Pages 467-467 Back Matter....Pages 469-472