Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory.ï¿½Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.
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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 ????????Norm 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
AuthorsRobert B. Gardner Professor of Mathematics and Statistics, Department of Mathematics and Statistics, East Tennessee State University, TN, USA. 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. Narendra K. Govil Professor Emeritus in the Department of Mathematics and Statistics, Auburn University, AL, USA. Narendra K. Govil is Professor Emeritus in the Department of Mathematics and Statistics at Auburn University, from where he retired as Professor, in 2020. He received his M.Sc. from Aligarh Muslim University, India and Ph.D. from the University of Montreal, Canada. He is a Fellow of the National Academy of Sciences, India and has been Alumni Professor in Department of Mathematics and Statistics at Auburn University. Before joining Auburn in 1983, he was a Professor at Indian Institute of Technology (IIT), New Delhi, India. He is a researcher in Complex Analysis and Approximation Theory, and has written a large number of papers in subjects related to Bernstein-type Inequalities, Geometry of the Zeros of Polynomials, Special Functions, and Wavelets. He is presently serving as Editor/Associate Editor of several journals, and has co-authored/co-edited six books including Progress in Approximation Theory and Applicable Complex Analysis, published by Springer in 2017. Gradimir V. Milovanovic Professor of Numerical Analysis and Approximation Theory and Full Member, Serbian Academy of Sciences and Arts, Beograd, Serbia. Gradimir V. Milovanovic 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 Nis, 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 Nis (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 Milovanovic are Topics in Polynomials: Extremal Problems, Inequalities, Zeros (coauthors: D. S. Mitrinovic 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 (c??uthor: G. Mastroianni) by Springer, 2008. (Home page: http://www.mi.sanu.ac.rs/~gvm/ ). 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 Mathï¿½matique, Mathematical Institute, Belgrade, etc.).