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Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials
 - 1st Edition - ISBN: 9780128119884

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

1st Edition

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Authors: Robert B. Gardner Narendra K. Govil Gradimir V. Milovanović
Paperback ISBN: 9780128119884
Imprint: Academic Press
Published Date: 1st May 2021
Page Count: 304
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Table of Contents

1. History and Introduction of Markov and Bernstein Inequalities
2. Bernstein-Type Inequalities for Polynomials with Restricted Zero
3. Bernstein-Type Inequalities in 𝐿𝐿𝑝𝑝Norm
4. Bernstein-Type Inequalities for Polar Derivatives of Polynomials
5. Bernstein-Type Inequalities for Rational Functions
6. Bernstein-Type Inequalities for Entire Functions of Exponential Type


Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.

Key Features

  • Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary
  • Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions
  • Contains exhaustive references with thousands of citations to articles and books
  • Features methods to solve inverse problems across approximation theory
  • Includes open problems for further research


Graduate students and 1st year PhDs working in mathematical analysis and approximation theory, especially in geometry of polynomials and complex approximation


No. of pages:
© Academic Press 2021
1st May 2021
Academic Press
Paperback ISBN:

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About the Authors

Robert B. Gardner

Robert Gardner is a tenured Professor of Mathematics and Statistics at East Tennessee State University specializing in Bernstein-type inequalities. He has co-authored/co-edited two books, including Real Analysis with an Introduction to Wavelets and Applications that was published by Elsevier in 2005.

Affiliations and Expertise

Department of Mathematics and Statistics, East Tennessee State University, TN, USA

Narendra K. Govil

Narendra Govil is Alumni Professor and Associate Chair of Mathematics and Statistics at Auburn State College. He is a researcher in Complex Analysis and has written a large number of papers related to Bernstein-type inequalities. He has co co-edited four books.

Affiliations and Expertise

Professor and Associate Chair of Mathematics and Statistics, Auburn State College, AL, USA

Gradimir V. Milovanović

Gradimir V. Milovanović is a Professor of Numerical Analysis and Approximation Theory and Full Member of the Serbian Academy of Sciences and Arts. He studied at University of Niš, obtaining a B.Sc. (1971) in electrical engineering and computer sciences and an M.Sc. (1974) and a Ph.D. (1976) in mathematics. He was with the Faculty of Electronic Engineering and the Department of Mathematics at the same place as, promoted to professor (1986) and acting as Dean of the Faculty of Electronic Engineering (2002-2004) and Rector of the University of Niš (2004–06), as well as Dean of the Faculty of Computer Sciences at the Megatrend University, Belgrade (2008-2011), until he joined the Mathematical Institute of the Serbian Academy of Sciences and Arts in Belgrade (2011). He was President of the National Council for Scientific and Technological Development of the Republic of Serbia (2006-2010). His research interests are Orthogonal Polynomials and Systems; Interpolation, Quadrature Processes and Integral Equations; Approximation by Polynomials and Splines; Extremal Problems, Inequalities and Zeros of Polynomials. He published 7 monographs, about 250 scientific papers in refereed journals, 35 book chapters, about 50 papers in conference proceedings, as well as 20 textbooks. Most significant monograph works of Milovanović are Topics in Polynomials: Extremal Problems, Inequalities, Zeros (coauthors: D. S. Mitrinović and Th. M. Rassias), published at over 800 pages by World Scientific (Singapore, 1994) and known in the world as „Bible of Polynomials“ and the monograph Interpolation Processes – Basic Theory and Applications (cоаuthor: G. Mastroianni) by Springer, 2008. (Home page: ). He is currently serving as an Editor-in-Chief and an Associate Editor for several journals (Journal of Inequalities and Applications, Springer; Optimization Letters, Springer; Applied Mathematics and Computation, Elsevier; Publications de l’Institut Mathématique, Mathematical Institute, Belgrade, etc.).

Affiliations and Expertise

Serbian Academy of Sciences and Arts