Analytic and Geometric Inequalities and Applications

✍ Scribed by Tsuyoshi Ando (auth.), Themistocles M. Rassias, Hari M. Srivastava (eds.)

• Publisher: Springer Netherlands
• Year: 1999
• Tongue: English
• Leaves: 376
• Series: Mathematics and Its Applications 478
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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
Second Order Opial Inequalities in $${\mathcal{L}^p}$$ Spaces and Applications....Pages 37-52
On Multi-Dimensional Integral Inequalities and Applications....Pages 53-67
Some Inequalities for Triangle: Old and New Results....Pages 69-92
A Treatise on Grüss’ Inequality....Pages 93-113
A ≥ B ≥ 0 Ensures $${\left( {{B^{\frac{r}{2}}}{A^p}{B^{\frac{r}{2}}}} \right)^{\frac{1}{q}}} \geqslant {\left( {{B^{\frac{r}{2}}}{A^p}{B^{\frac{r}{2}}}} \right)^{\frac{1}{q}}}$$ for R ≥ 0, P ≥ 0, G ≥ 1 with (1 + R)Q ≥P + R and its Recent Appications....Pages 115-134
Degree of Convergence for a Class of Linear Operators....Pages 135-150
Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory....Pages 151-181
Fractional Order Inequalities of Hardy Type....Pages 183-189
Theory of Differential and Integral Inequalities with Initial Time Difference and Applications....Pages 191-203
Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials....Pages 205-229
Bounds on Entropy Measures for Mixed Populations....Pages 231-244
Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials....Pages 245-264
On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions....Pages 265-276
Fourth Order Obstacle Boundary Value Problems....Pages 277-300
On Some Generalized Opial Type Inequalities....Pages 301-322
Controlling the Velocity of Brownian Motion by its Terminal Value....Pages 323-333
Chebyshev Polynomials with Integer Coefficients....Pages 335-348
Distortion Inequalities for Analytic and Univalent Functions Associated with Certain Fractional Calculus and other Linear Operators....Pages 349-374
Back Matter....Pages 375-377

✦ Subjects

Real Functions; Functions of a Complex Variable; Special Functions; Integral Transforms, Operational Calculus; Functional Analysis