Academic Press Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials (Mathematical Analysis and its Applications)

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. 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 Review Presents a self-contained, deep and clear presentation of current applied research in Bernstein-type inequalities From the Back Cover <p>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. Here, not only <i>Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials</i>, 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.</p> About the Author 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 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. 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