Analytic and Geometric Inequalities and Applications

1. Front Matter

   Pages i-vii

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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

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.

• convolution
• functional analysis
• integral transform
• operational calculus

• 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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