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.
Tabella dei contenuti
Inequalities Related to Ordinary and Partial Differential Equations.- A Rayleigh-Faber-Krahn Inequality and Some Monotonicity Properties for Eigenvalue Problems with Mixed Boundary Conditions.- Lower and Upper Bounds for Sloshing Frequencies.- On Spectral Bounds for Photonic Crystal Waveguides.- Real Integrability Conditions for the Nonuniform Exponential Stability of Evolution Families on Banach Spaces.- Validated Computations for Fundamental Solutions of Linear Ordinary Differential Equations.- Integral Inequalities.- Equivalence of Modular Inequalities of Hardy Type on Non-negative Respective Non-increasing Functions.- Some One Variable Weighted Norm Inequalities and Their Applications to Sturm-Liouville and Other Differential Operators.- Bounding the Gini Mean Difference.- On Some Integral Inequalities.- A New Characterization of the Hardy and Its Limit Pólya-Knopp Inequality for Decreasing Functions.- Euler-Grüss Type Inequalities Involving Measures.- The ?-quasiconcave Functions and Weighted Inequalities.- Inequalities for Operators.- Inequalities for the Norm and Numerical Radius of Composite Operators in Hilbert Spaces.- Norm Inequalities for Commutators of Normal Operators.- Uniformly Continuous Superposition Operators in the Spaces of Differentiable Functions and Absolutely Continuous Functions.- Tight Enclosures of Solutions of Linear Systems.- Inequalities in Approximation Theory.- Operators of Bernstein-Stancu Type and the Monotonicity of Some Sequences Involving Convex Functions.- Inequalities Involving the Superdense Unbounded Divergence of Some Approximation Processes.- An Overview of Absolute Continuity and Its Applications.- Generalizations of Convexity and Inequalities for Means.- Normalized Jensen Functional, Superquadracity and Related Inequalities.- Comparability of Certain Homogeneous Means.- On Some General Inequalities Related to Jensen’s Inequality.- Schur-Convexity, Gamma Functions, and Moments.- A Characterization of Nonconvexity and Its Applications in the Theory of Quasi-arithmetic Means.- Approximately Midconvex Functions.- Inequalities, Stability, and Functional Equations.- Sandwich Theorems for Orthogonally Additive Functions.- On Vector Pexider Differences Controlled by Scalar Ones.- A Characterization of the Exponential Distribution through Functional Equations.- Approximate Solutions of the Linear Equation.- On a Functional Equation Containing Weighted Arithmetic Means.
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