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Full Description
Analytic and Geometric Inequalities and Applications is devoted to recent advances in a variety of inequalities of Mathematical Analysis and Geo metry. Subjects dealt with in this volume include: Fractional order inequalities of Hardy type, differential and integral inequalities with initial time differ ence, multi-dimensional integral inequalities, Opial type inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and applications in statistics and matrix theory, distortion inequalities for ana lytic and univalent functions associated with certain fractional calculus and other linear operators, problem of infimum in the positive cone, alpha-quasi convex functions defined by convolution with incomplete beta functions, Chebyshev polynomials with integer coefficients, extremal problems for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of some companion matrices and bounds for the zeros of polynomials, degree of convergence for a class of linear operators, open problems on eigenvalues of the Laplacian, fourth order obstacle boundary value problems, bounds on entropy measures for mixed populations as well as controlling the velocity of Brownian motion by its terminal value. A wealth of applications of the above is also included. We wish to express our appreciation to the distinguished mathematicians who contributed to this volume. Finally, it is our pleasure to acknowledge the fine cooperation and assistance provided by the staff of Kluwer Academic Publishers. June 1999 Themistocles M. Rassias Hari M.
Contents
Problem of Infimum in the Positive Cone.- Open Problems on Eigenvalues of the Laplacian.- On an Inequality of S. Bernstein and the Gauss-Lucas Theorem.- Second Order Opial Inequalities in Lp Spaces and Applications.- On Multi-Dimensional Integral Inequalities and Applications.- Some Inequalities for Triangle: Old and New Results.- A Treatise on Grüss' Inequality.- A?B?0Ensures (Br/2Ar/2Br/2)1/q ? (Br/2Br/2Br/2)1/q for r?0,p?0, q ? 1 with (1+r)q ? p + r and its Recent Applications.- Degree of Convergence for a Class of Linear Operators.- Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory.- Fractional Order Inequalities of Hardy Type.- Theory of Differential and Integral Inequalities with Initial Time Difference and Applications.- Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials.- Bounds on Entropy Measures for Mixed Populations.- Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials.- On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions.- Fourth Order Obstacle Boundary Value Problems.- On Some Generalized Opial Type Inequalities.- Controlling the Velocity of Brownian Motion by its Terminal Value.- Chebyshev Polynomials with Integer Coefficients.- Distortion Inequalities for Analytic and Univalent Functions Associated with Certain Fractional Calculus and Other Linear Operators.
