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Analytic and Geometric Inequalities and Applications

  • Book
  • © 1999

Overview

Editors:
  1. Themistocles M. Rassias

    1. Department of Mathematics, National Technical University of Athens, Athens, Greece

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    You can also search for this editor in PubMed   Google Scholar

  2. Hari M. Srivastava

    1. Department of Mathematics and Statistics, University of Victoria, Victoria, Canada

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 478)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Problem of Infimum in the Positive Cone

    • Tsuyoshi Ando
    Pages 1-12

  3. Open Problems on Eigenvalues of the Laplacian

    • Mark S. Ashbaugh
    Pages 13-28

  4. On an Inequality of S. Bernstein and the Gauss-Lucas Theorem

    • A. Aziz, N. A. Rather
    Pages 29-35

  5. Second Order Opial Inequalities in \({\mathcal{L}^p}\) Spaces and Applications

    • Richard Brown, Victor Burenkov, Steve Clark, Don Hinton
    Pages 37-52

  6. On Multi-Dimensional Integral Inequalities and Applications

    • Wing-Sum Cheung, Themistocles M. Rassias
    Pages 53-67

  7. Some Inequalities for Triangle: Old and New Results

    • Radosav Ž. Djordjević
    Pages 69-92

  8. A Treatise on Grüss’ Inequality

    • A. M. Fink
    Pages 93-113

  9. 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

    • Takayuki Furuta
    Pages 115-134

  10. Degree of Convergence for a Class of Linear Operators

    • N. K. Govil, R. N. Mohapatra
    Pages 135-150

  11. Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory

    • Shane T. Jensen, George P. H. Styan
    Pages 151-181

  12. Fractional Order Inequalities of Hardy Type

    • Alois Kufner
    Pages 183-189

  13. Theory of Differential and Integral Inequalities with Initial Time Difference and Applications

    • V. Lakshmikantham, A. S. Vatsala
    Pages 191-203

  14. Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials

    • Hansjörg Linden
    Pages 205-229

  15. Bounds on Entropy Measures for Mixed Populations

    • M. Matić, C. E. M. Pearce, J. Pečarić
    Pages 231-244

  16. Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials

    • Gradimir V. Milovanović
    Pages 245-264

  17. On Alpha-Quasi-Convex Functions Defined by Convolution with Incomplete Beta Functions

    • Khalida Inayat Noor
    Pages 265-276

  18. Fourth Order Obstacle Boundary Value Problems

    • Muhammad Aslam Noor, Eisa A. Al-Said
    Pages 277-300

  19. On Some Generalized Opial Type Inequalities

    • B. G. Pachpatte
    Pages 301-322

  20. Controlling the Velocity of Brownian Motion by its Terminal Value

    • Goran Peskir
    Pages 323-333
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  • Department of Mathematics and Statistics, University of Victoria, Victoria, Canada

    Hari M. Srivastava

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