Ebook: Analytic and Geometric Inequalities and Applications
- Tags: Real Functions, Functions of a Complex Variable, Special Functions, Integral Transforms Operational Calculus, Functional Analysis
- Series: Mathematics and Its Applications 478
- Year: 1999
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-vii
Problem of Infimum in the Positive Cone....Pages 1-12
Open Problems on Eigenvalues of the Laplacian....Pages 13-28
On an Inequality of S. Bernstein and the Gauss-Lucas Theorem....Pages 29-35
On Multi-Dimensional Integral Inequalities and Applications....Pages 37-52
Some Inequalities for Triangle: Old and New Results....Pages 53-67
A Treatise on Gr?ss’ Inequality....Pages 69-92
Degree of Convergence for a Class of Linear Operators....Pages 93-113
Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory....Pages 115-134
Fractional Order Inequalities of Hardy Type....Pages 135-150
Theory of Differential and Integral Inequalities with Initial Time Difference and Applications....Pages 151-181
Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials....Pages 183-189
Bounds on Entropy Measures for Mixed Populations....Pages 191-203
Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials....Pages 205-229
On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions....Pages 231-244
Fourth Order Obstacle Boundary Value Problems....Pages 245-264
On Some Generalized Opial Type Inequalities....Pages 265-276
Controlling the Velocity of Brownian Motion by its Terminal Value....Pages 277-300
Chebyshev Polynomials with Integer Coefficients....Pages 301-322
Back Matter....Pages 323-333
Distortion Inequalities for Analytic and Univalent Functions Associated with Certain Fractional Calculus and other Linear Operators....Pages 335-348
....Pages 375-377