Advanced Inequalities
eBook - PDF

Advanced Inequalities

  1. 424 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Advanced Inequalities

About this book

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, Gruss and Comparison of Means inequalities are studied.The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Advanced Inequalities by George A Anastassiou in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Contents
  2. Preface
  3. 1. Introduction
  4. 2. Advanced Univariate Ostrowski Type Inequalities
  5. 3. Higher Order Ostrowski Inequalities
  6. 4. Multidimensional Euler Identity and Optimal Multidimensional Ostrowski Inequalities
  7. 5. More on Multidimensional Ostrowski Type Inequalities
  8. 6. Ostrowski Inequalities on Euclidean Domains
  9. 7. High Order Ostrowski Inequalities on Euclidean Domains
  10. 8. Ostrowski Inequalities on Spherical Shells
  11. 9. Ostrowski Inequalities on Balls and Shells Via Taylor{Widder Formula
  12. 10. Multivariate Opial Type Inequalities for Functions Vanishing at an Interior Point
  13. 11. General Multivariate Weighted Opial Inequalities
  14. 12. Opial Inequalities for Widder Derivatives
  15. 13. Opial Inequalities for Linear Differential Operators
  16. 14. Opial Inequalities for Vector Valued Functions
  17. 15. Opial Inequalities for Semigroups
  18. 16. Opial Inequalities for Cosine and Sine Operator Functions
  19. 17. Poincare Like Inequalities for Linear Differential Operators
  20. 18. Poincare and Sobolev Like Inequalities for Widder Derivatives
  21. 19. Poincare and Sobolev Like Inequalities for Vector Valued Functions
  22. 20. Poincare Type Inequalities for Semigroups, Cosine and Sine Operator Functions
  23. 21. Hardy–Opial Type Inequalities
  24. 22. A Basic Sharp Integral Inequality
  25. 23. Estimates of the Remainder in Taylor's Formula
  26. 24. The Distributional Taylor Formula
  27. 25. Chebyshev–Gruss Type Inequalities Using Euler Type and Fink Identities
  28. 26. Gruss Type Multivariate Integral Inequalities
  29. 27. Chebyshev–Gruss Type Inequalities on Spherical Shells and Balls
  30. 28. Multivariate Chebyshev–Gruss and Comparison of Integral Means Inequalities
  31. 29. Multivariate Fink Type Identity Applied to Multivariate Inequalities
  32. Bibliography
  33. List of Symbols
  34. Index