Ebook: Inequalities and Applications: Conference on Inequalities and Applications, Noszvaj (Hungary), September 2007

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pólya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics.

This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.

---

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and P?lya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics.

This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.

---

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and P?lya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics.

This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.

Content:
Front Matter....Pages i-xlviii
Front Matter....Pages 1-1
A Rayleigh-Faber-Krahn Inequality and Some Monotonicity Properties for Eigenvalue Problems with Mixed Boundary Conditions....Pages 3-12
Lower and Upper Bounds for Sloshing Frequencies....Pages 13-22
On Spectral Bounds for Photonic Crystal Waveguides....Pages 23-30
Real Integrability Conditions for the Nonuniform Exponential Stability of Evolution Families on Banach Spaces....Pages 31-42
Validated Computations for Fundamental Solutions of Linear Ordinary Differential Equations....Pages 43-50
Front Matter....Pages 51-51
Equivalence of Modular Inequalities of Hardy Type on Non-negative Respective Non-increasing Functions....Pages 53-59
Some One Variable Weighted Norm Inequalities and Their Applications to Sturm-Liouville and Other Differential Operators....Pages 61-76
Bounding the Gini Mean Difference....Pages 77-89
On Some Integral Inequalities....Pages 91-95
A New Characterization of the Hardy and Its Limit P?lya-Knopp Inequality for Decreasing Functions....Pages 97-107
Euler-Gr?ss Type Inequalities Involving Measures....Pages 109-120
The ?-quasiconcave Functions and Weighted Inequalities....Pages 121-132
Front Matter....Pages 133-133
Inequalities for the Norm and Numerical Radius of Composite Operators in Hilbert Spaces....Pages 135-146
Norm Inequalities for Commutators of Normal Operators....Pages 147-154
Uniformly Continuous Superposition Operators in the Spaces of Differentiable Functions and Absolutely Continuous Functions....Pages 155-166
Tight Enclosures of Solutions of Linear Systems....Pages 167-178
Front Matter....Pages 179-179
Operators of Bernstein-Stancu Type and the Monotonicity of Some Sequences Involving Convex Functions....Pages 181-192
Inequalities Involving the Superdense Unbounded Divergence of Some Approximation Processes....Pages 193-200
An Overview of Absolute Continuity and Its Applications....Pages 201-214
Front Matter....Pages 215-215
Normalized Jensen Functional, Superquadracity and Related Inequalities....Pages 217-228
Front Matter....Pages 215-215
Comparability of Certain Homogeneous Means....Pages 229-232
On Some General Inequalities Related to Jensen’s Inequality....Pages 233-243
Schur-Convexity, Gamma Functions, and Moments....Pages 245-250
A Characterization of Nonconvexity and Its Applications in the Theory of Quasi-arithmetic Means....Pages 251-260
Approximately Midconvex Functions....Pages 261-265
Front Matter....Pages 267-267
Sandwich Theorems for Orthogonally Additive Functions....Pages 269-281
On Vector Pexider Differences Controlled by Scalar Ones....Pages 283-290
A Characterization of the Exponential Distribution through Functional Equations....Pages 291-298
Approximate Solutions of the Linear Equation....Pages 299-304
On a Functional Equation Containing Weighted Arithmetic Means....Pages 305-315

---

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and P?lya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics.

This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.

Content:
Front Matter....Pages i-xlviii
Front Matter....Pages 1-1
A Rayleigh-Faber-Krahn Inequality and Some Monotonicity Properties for Eigenvalue Problems with Mixed Boundary Conditions....Pages 3-12
Lower and Upper Bounds for Sloshing Frequencies....Pages 13-22
On Spectral Bounds for Photonic Crystal Waveguides....Pages 23-30
Real Integrability Conditions for the Nonuniform Exponential Stability of Evolution Families on Banach Spaces....Pages 31-42
Validated Computations for Fundamental Solutions of Linear Ordinary Differential Equations....Pages 43-50
Front Matter....Pages 51-51
Equivalence of Modular Inequalities of Hardy Type on Non-negative Respective Non-increasing Functions....Pages 53-59
Some One Variable Weighted Norm Inequalities and Their Applications to Sturm-Liouville and Other Differential Operators....Pages 61-76
Bounding the Gini Mean Difference....Pages 77-89
On Some Integral Inequalities....Pages 91-95
A New Characterization of the Hardy and Its Limit P?lya-Knopp Inequality for Decreasing Functions....Pages 97-107
Euler-Gr?ss Type Inequalities Involving Measures....Pages 109-120
The ?-quasiconcave Functions and Weighted Inequalities....Pages 121-132
Front Matter....Pages 133-133
Inequalities for the Norm and Numerical Radius of Composite Operators in Hilbert Spaces....Pages 135-146
Norm Inequalities for Commutators of Normal Operators....Pages 147-154
Uniformly Continuous Superposition Operators in the Spaces of Differentiable Functions and Absolutely Continuous Functions....Pages 155-166
Tight Enclosures of Solutions of Linear Systems....Pages 167-178
Front Matter....Pages 179-179
Operators of Bernstein-Stancu Type and the Monotonicity of Some Sequences Involving Convex Functions....Pages 181-192
Inequalities Involving the Superdense Unbounded Divergence of Some Approximation Processes....Pages 193-200
An Overview of Absolute Continuity and Its Applications....Pages 201-214
Front Matter....Pages 215-215
Normalized Jensen Functional, Superquadracity and Related Inequalities....Pages 217-228
Front Matter....Pages 215-215
Comparability of Certain Homogeneous Means....Pages 229-232
On Some General Inequalities Related to Jensen’s Inequality....Pages 233-243
Schur-Convexity, Gamma Functions, and Moments....Pages 245-250
A Characterization of Nonconvexity and Its Applications in the Theory of Quasi-arithmetic Means....Pages 251-260
Approximately Midconvex Functions....Pages 261-265
Front Matter....Pages 267-267
Sandwich Theorems for Orthogonally Additive Functions....Pages 269-281
On Vector Pexider Differences Controlled by Scalar Ones....Pages 283-290
A Characterization of the Exponential Distribution through Functional Equations....Pages 291-298
Approximate Solutions of the Linear Equation....Pages 299-304
On a Functional Equation Containing Weighted Arithmetic Means....Pages 305-315
....