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

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

by Robert Gardner,Narendra Govil,Gradimir V. Milovanovic

  • Publisher : Academic Press
  • Release : 2019-11-15
  • Pages : 304
  • ISBN : 9780128119884
  • Language : En, Es, Fr & De
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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 Polynomials

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

by Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanović

  • Publisher : Academic Press
  • Release : 2020-11-01
  • Pages : 304
  • ISBN : 012812007X
  • Language : En, Es, Fr & De
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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

Approximation Theory

Approximation Theory
In Memory of A.K. Varma

by Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados

  • Publisher : CRC Press
  • Release : 2021-02-01
  • Pages : 552
  • ISBN : 1000146030
  • Language : En, Es, Fr & De
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"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."

Mathematical Reviews

Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Topics in Polynomials

Topics in Polynomials
Extremal Problems, Inequalities, Zeros

by G V Milovanovic,D S Mitrinovic,Th M Rassias

  • Publisher : World Scientific
  • Release : 1994-06-28
  • Pages : 836
  • ISBN : 9814506486
  • Language : En, Es, Fr & De
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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 opinion, they have been greatly successful. The book would be useful not only for the specialist mathematician, but also for those researchers in the applied and computational sciences who use polynomials as a tool.” Mathematical Reviews “This is a remarkable book, offering a cornucopia of results, all connected by their involvement with polynomials. The scope of the volume can be conveyed by citing some statistics: there are 821 pages, 7 chapters, 20 sections, 108 subsections, 95 pages of references (distributed throughout the book), a name index of 16 pages, and a subject index of 19 pages … The book is written in a gentle style: one can open it anywhere and begin to understand, without encountering unfamiliar notation and terminology. It is strongly recommended to individuals and to libraries.” Mathematics of Computation “This book contains some of the most important results on the analysis of polynomials and their derivatives … is intended, not only for the specialist mathematician, but also for those researchers in the applied sciences who use polynomials as a tool.” Sever S Dragomir “This is a well-written book on a widely useful topic. It is strongly recommended not only to the mathematical specialist, but also to all those researchers in the applied and computational sciences who make frequent use of polynomials as a tool. Of course, libraries will also benefit greatly by including this book in their cherished collection.” Mathematics Abstracts “There is no doubt that this is a very useful work compiling enormous researches carried out on the subject … This is a well-written book on a widely useful topic.” Zentralblatt für Mathematik

Generalized Functions and Convergence

Generalized Functions and Convergence
Memorial Volume for Professor Jan MikusinskiProceedings of the Conference

by Piotr Antosik,Andrzej Kamiński

  • Publisher : World Scientific
  • Release : 1990-09-12
  • Pages : 396
  • ISBN : 9814611719
  • Language : En, Es, Fr & De
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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

Topics in Polynomials of One and Several Variables and Their Applications
Volume Dedicated to the Memory of P.L. Chebyshev (1821-1894)

by Themistocles M. Rassias,H. M. Srivastava

  • Publisher : World Scientific
  • Release : 1993
  • Pages : 638
  • ISBN : 9789810206147
  • Language : En, Es, Fr & De
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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

Approximation and Computation
In Honor of Gradimir V. Milovanović

by Walter Gautschi,Giuseppe Mastroianni,Themistocles M. Rassias

  • Publisher : Springer Science & Business Media
  • Release : 2010-10-20
  • Pages : 482
  • ISBN : 1441965947
  • Language : En, Es, Fr & De
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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.

Algebras, Groups, and Geometries

Algebras, Groups, and Geometries
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1996
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Recent Progress in Inequalities

Recent Progress in Inequalities
A Book

by G.V. Milovanovic

  • Publisher : Springer Science & Business Media
  • Release : 1998-01-31
  • Pages : 524
  • ISBN : 9780792348450
  • Language : En, Es, Fr & De
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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.

Journal of Natural Geometry

Journal of Natural Geometry
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1994
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Approximation Theory

Approximation Theory
A Volume Dedicated to Borislav Bojanov

by Dimitar K. Dimitrov,Borislav D. Bojanov

  • Publisher : Akademicno Izdatelstvo
  • Release : 2004
  • Pages : 338
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This volume is dedicated to the sixtieth anniversary of Professor Borislav Bojanov. It is a collection of twenty-one papers, written by highly respected colleagues and friends as well as by some of his former students. Contents include: On Jackson's Inequalities for Approximations in L2 of Periodic Functions by Trigonometric Polynomials and of Functions on the Line by Entire Functions; The Olovyanishnikov Inequality for Multivariate Functions; Bernstein-Durrmeyer Type Quasi-Interpolants on Intervals; Adaptive Approximation of Curves; An Efficient Definition of the Divided Difference; Extended Cubature Formula of Turan Type (0,2) for the Ball, The Multivariate Fundamental Theorem of Algebra, Bezout's Theorem and Nullstellensatz, Canonical Point Sets for Best One-Sided L1-Approximation by Quasi-Blending Functions, A Characterization Theorem for the K-functional for Kantorovich and Durrmeyer Operators, Some Error Estimates in Learning Theory, B-Spaces and their Characterization via Anistropic Franklin Bases; On Optimal Recovery of Heat Equation Solutions; Markov's Inequalities in Integral Norm for Oscillating Weighted Polynomials; Standard and non-standard quadratures of Gaussian Type; Inequalities for Real-Root Polynomials; On Smooth Interpolation; Thoughts over the Smale's Mean Value Conjecture; Twelve Proofs of the Markov Inequality; New Technique for Error Analysis of Finite Element Approximations of Parabolic Problems with Non-Smooth Initial Data; On Generalized Tractability for Multivariate Problems; On Polynomial Interpolation on the Unit Ball.

General Inequalities 6

General Inequalities 6
6th International Conference on General Inequalities, Oberwolfach, Dec. 9–15, 1990

by Wolfgang Walter

  • Publisher : Birkhäuser
  • Release : 2013-11-11
  • Pages : 508
  • ISBN : 3034875657
  • Language : En, Es, Fr & De
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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.

Orthogonal Functions

Orthogonal Functions
Moment Theory and Continued Fractions

by William Jones

  • Publisher : CRC Press
  • Release : 2020-12-23
  • Pages : 329
  • ISBN : 1000153673
  • Language : En, Es, Fr & De
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"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."

Extremal Properties of Polynomials and Splines

Extremal Properties of Polynomials and Splines
A Book

by Nikolaĭ Pavlovich Korneĭchuk,Anatoliĭ Aleksandrovich Ligun,V. F. Babenko

  • Publisher : Nova Publishers
  • Release : 1996
  • Pages : 433
  • ISBN : 9781560723615
  • Language : En, Es, Fr & De
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Extremal Properties of Polynomials & Splines

Journal of Contemporary Mathematical Analysis

Journal of Contemporary Mathematical Analysis
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2001
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Generalized Functions and Convergence

Generalized Functions and Convergence
Memorial Volume for Professor Jan Mikusiński ; 13-18 June 1988, Katowice, Poland

by Piotr Antosik,Andrzej Kamiński

  • Publisher : World Scientific Publishing Company Incorporated
  • Release : 1990
  • Pages : 386
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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.

Probability Theory, Function Theory, Mechanics

Probability Theory, Function Theory, Mechanics
A Book

by Jurij V. Prochorov

  • Publisher : American Mathematical Soc.
  • Release : 1990
  • Pages : 317
  • ISBN : 9780821831328
  • Language : En, Es, Fr & De
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This is a translation of the fifth and final volume in a special cycle of publications in commemoration of the 50th anniversary of the Steklov Mathematical Institute of the Academy of Sciences in the USSR. The purpose of the special cycle was to present surveys of work on certain important trends and problems pursued at the Institute. Because the choice of the form and character of the surveys were left up to the authors, the surveys do not necessarily form a comprehensive overview, but rather represent the authors' perspectives on the important developments. The survey papers in this collection range over a variety of areas, including - probability theory and mathematical statistics, metric theory of functions, approximation of functions, descriptive set theory, spaces with an indefinite metric, group representations, mathematical problems of mechanics and spaces of functions of several real variables and some applications.

Transactions of the American Mathematical Society

Transactions of the American Mathematical Society
A Book

by American Mathematical Society

  • Publisher : Unknown Publisher
  • Release : 1995
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Handbook of Functional Equations

Handbook of Functional Equations
Functional Inequalities

by Themistocles M. Rassias

  • Publisher : Springer
  • Release : 2014-11-18
  • Pages : 555
  • ISBN : 1493912461
  • Language : En, Es, Fr & De
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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.