Ebook: Inequalities and Applications 2010: Dedicated to the Memory of Wolfgang Walter

Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970’s and has generated a vast variety of further research in this field. He also organized six of the seven “General Inequalities” Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the “General Inequalities 8” conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter’s memory. The “General Inequalities” meetings found their continuation in the “Conferences on Inequalities and Applications” which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajdúszoboszló in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.

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Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970’s and has generated a vast variety of further research in this field. He also organized six of the seven “General Inequalities” Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the “General Inequalities 8” conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter’s memory. The “General Inequalities” meetings found their continuation in the “Conferences on Inequalities and Applications” which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajd?szoboszl? in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.

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Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970’s and has generated a vast variety of further research in this field. He also organized six of the seven “General Inequalities” Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the “General Inequalities 8” conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter’s memory. The “General Inequalities” meetings found their continuation in the “Conferences on Inequalities and Applications” which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajd?szoboszl? in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.

Content:
Front Matter....Pages I-LXX
Front Matter....Pages 1-1
Domain Derivatives for Energy Functionals with Boundary Integrals....Pages 3-17
The Asymptotic Shape of a Boundary Layer of Symmetric Willmore Surfaces of Revolution....Pages 19-29
A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem....Pages 31-52
Green Function Estimates Lead to Neumann Function Estimates....Pages 53-63
Front Matter....Pages 65-65
Deriving Inequalities in the Laguerre-P?lya Class from Properties of Half-Plane Mappings....Pages 67-86
Fundamental Error Estimate Inequalities for the Tikhonov Regularization Using Reproducing Kernels....Pages 87-101
On the Approximation-Error of Some Numerical Methods for Obtaining the Optimal Deformable Model....Pages 103-115
Front Matter....Pages 117-117
The Longest Shortest Piercing....Pages 119-124
On a Continuous Mapping and Sharp Triangle Inequalities....Pages 125-136
A Dunkl-Williams Inequality and the Generalized Operator Version....Pages 137-148
Front Matter....Pages 149-149
Jordan Type Representation of Functions with Generalized High Order Bounded Variation....Pages 151-163
On Vector Hermite-Hadamard Differences Controlled by Their Scalar Counterparts....Pages 165-173
Functions Generating Strongly Schur-Convex Sums....Pages 175-182
Strongly Convex Sequences....Pages 183-188
Front Matter....Pages 189-189
Refinement of Inequalities Related to Convexity via Superquadracity, Weaksuperquadracity and Superterzacity....Pages 191-207
On Two Different Concepts of Subquadraticity....Pages 209-215
Connections Between the Jensen and the Chebychev Functionals....Pages 217-227
Front Matter....Pages 229-229
Functional Inequalities and Equivalences of Some Estimates....Pages 231-240
On Measurable Functions Satisfying Multiplicative Type Functional Equations Almost Everywhere....Pages 241-253
Quasimonotonicity as a Tool for Differential and Functional Inequalities....Pages 255-268
....Pages 269-273