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

Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomials


  • Author : Robert B. Gardner
  • Publisher : Elsevier
  • Release Date : 2022-02-15
  • Genre: Mathematics
  • Pages : 442
  • ISBN 10 : 9780128119884

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Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomials Excerpt :

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

Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomial Book

Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomial


  • Author : Robert B. Gardner
  • Publisher : Academic Press
  • Release Date : 2022-03-14
  • Genre: Mathematics
  • Pages : 442
  • ISBN 10 : 9780128120071

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Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomial Excerpt :

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 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. Applies Markov-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, and entire functions of exponential type Contains exhaustive references with more than five hundred citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research

Topics in Polynomials Book

Topics in Polynomials


  • Author : G V Milovanovic
  • Publisher : World Scientific
  • Release Date : 1994-06-28
  • Genre: Science
  • Pages : 836
  • ISBN 10 : 9789814506489

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Topics in Polynomials Excerpt :

The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution. Contents:PrefaceGeneral Concept of Algebraic PolynomialsSelected Polynomial InequalitiesZeros of PolynomialsInequalities Connected with Trigonometric SumsExtremal Problems for PolynomialsExtremal Problems of Markov-Bernstein TypeSome Applications of PolynomialsSymbol IndexName IndexSubject Index Readership: Mathematicians and mathematical physicists. keywords:Algebraic Polynomials;Trigonometric Polynomials;Zeros;Extremal Problems;Trigonometric Sums;Positivity and Monotonicity;Distribution of Zeros;Bounds for Polynomial Zeros;Incomplete Polynomials;Polynomials with Minimal Norm;Markov-Bernstein Inequalities;Approximation;Symmetric Functions;Orthogonal Polynomials;Nonnegative Polynomials “The topics are tastefully selected and the results are easy to find. Although this book is not really planned as a textbook to teach from, it is excellent for self-study or seminars. This is a very useful reference book with many results which have not appeared in a book form yet. It is an important addition to the literature.” Journal of Approximation Theory “I find the book to be well written and readable. The authors have made an attempt to present the material in an integrated and self-contained fashion and, in my o

Approximation Theory Book

Approximation Theory


  • Author : Narenda Govil
  • Publisher : CRC Press
  • Release Date : 2021-02-01
  • Genre: Mathematics
  • Pages : 551
  • ISBN 10 : 9781000146035

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Approximation Theory Excerpt :

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Generalized Functions and Convergence Book

Generalized Functions and Convergence


  • Author : Piotr Antosik
  • Publisher : World Scientific
  • Release Date : 1990-09-12
  • Genre: Uncategoriezed
  • Pages : 396
  • ISBN 10 : 9789814611718

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Generalized Functions and Convergence Excerpt :

The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures. Contents:On Uniform Convergence of the Inner Product of Sequences (P Antosik et al)Decompositions of F-spaces into spaces with Properties K, N or k (J Burzyk)Finite Integral Transforms for Non-Local Boundary Value Problems (I H Dimovski & R I Petrova) On the Neutrix Convolution Product xs * xλ+ (B Fisher)On the Wiener-Laguerre Transform of Generalized Functions (H J Glaeske)On Distributional Solutions of the Generalized Entropy Equation (A Kaminski)On a Representation of the Algebra o of Mikusinski Operators (C Klis)Semilinear Wave Equations with Rough Initial Data: Generalized Solutions (M Oberguggenberger)Prodigious Mystery of Genuine Analysis (D Przeworska-Rolewicz)Asymtotic Bounds for the Distributional Stieltjes Transforms (A Takaci)On Tensor Product and Convolution of Generalized Functions of Gelfand-Shilov Type (J Uryga)Multidimensional Tauberian Theorems for Distributions (V S Vladimirov et al)and others Readership: Mathematicians and mathematical physicists.

Topics in Polynomials of One and Several Variables and Their Applications Book

Topics in Polynomials of One and Several Variables and Their Applications


  • Author : Themistocles M. Rassias
  • Publisher : World Scientific
  • Release Date : 1993
  • Genre: Mathematics
  • Pages : 660
  • ISBN 10 : 9810206143

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Topics in Polynomials of One and Several Variables and Their Applications Excerpt :

This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.

Approximation and Computation Book

Approximation and Computation


  • Author : Walter Gautschi
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-10-20
  • Genre: Mathematics
  • Pages : 482
  • ISBN 10 : 9781441965943

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Approximation and Computation Excerpt :

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.

Analytic and Geometric Inequalities and Applications Book

Analytic and Geometric Inequalities and Applications


  • Author : Themistocles RASSIAS
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 377
  • ISBN 10 : 9789401145770

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Analytic and Geometric Inequalities and Applications Excerpt :

Analytic and Geometric Inequalities and Applications is devoted to recent advances in a variety of inequalities of Mathematical Analysis and Geo metry. Subjects dealt with in this volume include: Fractional order inequalities of Hardy type, differential and integral inequalities with initial time differ ence, multi-dimensional integral inequalities, Opial type inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and applications in statistics and matrix theory, distortion inequalities for ana lytic and univalent functions associated with certain fractional calculus and other linear operators, problem of infimum in the positive cone, alpha-quasi convex functions defined by convolution with incomplete beta functions, Chebyshev polynomials with integer coefficients, extremal problems for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of some companion matrices and bounds for the zeros of polynomials, degree of convergence for a class of linear operators, open problems on eigenvalues of the Laplacian, fourth order obstacle boundary value problems, bounds on entropy measures for mixed populations as well as controlling the velocity of Brownian motion by its terminal value. A wealth of applications of the above is also included. We wish to express our appreciation to the distinguished mathematicians who contributed to this volume. Finally, it is our pleasure to acknowledge the fine cooperation and assistance provided by the staff of Kluwer Academic Publishers. June 1999 Themistocles M. Rassias Hari M.

Recent Progress in Inequalities Book

Recent Progress in Inequalities


  • Author : G.V. Milovanovic
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-14
  • Genre: Mathematics
  • Pages : 524
  • ISBN 10 : 9789401590860

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Recent Progress in Inequalities Excerpt :

This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.

Orthogonal Functions Book

Orthogonal Functions


  • Author : William Jones
  • Publisher : CRC Press
  • Release Date : 2020-12-22
  • Genre: Mathematics
  • Pages : 258
  • ISBN 10 : 9781000153675

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Orthogonal Functions Excerpt :

"Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."

General Inequalities 6 Book

General Inequalities 6


  • Author : Wolfgang Walter
  • Publisher : Birkhäuser
  • Release Date : 2013-11-11
  • Genre: Science
  • Pages : 508
  • ISBN 10 : 9783034875653

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General Inequalities 6 Excerpt :

The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities.

Generalized Functions and Convergence Book

Generalized Functions and Convergence


  • Author : Piotr Antosik
  • Publisher : World Scientific Publishing Company Incorporated
  • Release Date : 1990
  • Genre: Mathematics
  • Pages : 404
  • ISBN 10 : UCAL:B4406622

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Generalized Functions and Convergence Excerpt :

The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures.

Handbook of Functional Equations Book

Handbook of Functional Equations


  • Author : Themistocles M. Rassias
  • Publisher : Springer
  • Release Date : 2014-11-18
  • Genre: Mathematics
  • Pages : 555
  • ISBN 10 : 9781493912469

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Handbook of Functional Equations Excerpt :

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Mathematical Reviews Book

Mathematical Reviews


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2003
  • Genre: Mathematics
  • Pages : null
  • ISBN 10 : UVA:X006180631

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Mathematical Reviews Excerpt :

                                                       Book


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2000
  • Genre: Science
  • Pages : 626
  • ISBN 10 : STANFORD:36105025340733

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