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Inequalities

An Approach Through Problems

  • B. J. Venkatachala

Part of the Texts and Readings in Mathematics book series (TRIM, volume 49)

Table of contents

  1. Front Matter
    Pages i-xi
  2. B. J. Venkatachala
    Pages 1-49
  3. B. J. Venkatachala
    Pages 51-110
  4. B. J. Venkatachala
    Pages 111-171
  5. B. J. Venkatachala
    Pages 173-203
  6. B. J. Venkatachala
    Pages 205-244
  7. B. J. Venkatachala
    Pages 245-514
  8. Back Matter
    Pages 515-519

About this book

Introduction

This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications. 

Keywords

Chebyshev inequality geometric mean inequality arithmetic mean Cauchy-Schwarz inequality rearrangement inequality Muirhead's theorem

Authors and affiliations

  • B. J. Venkatachala
    • 1
  1. 1.Homi Bhabha Centre for Science Education (emeritus)MumbaiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-8732-5
  • Copyright Information Springer Nature Singapore Pte Ltd. and Hindustan Book Agency 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-981-10-8732-5
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • Buy this book on publisher's site