Advances In Summability And Approximation Theory
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Advances In Summability And Approximation Theory
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Author : S. A. Mohiuddine
language : en
Publisher: Springer
Release Date : 2018-12-30
Advances In Summability And Approximation Theory written by S. A. Mohiuddine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-30 with Mathematics categories.
This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
Advances In Applied Mathematics And Approximation Theory
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Advances In Applied Mathematics And Approximation Theory written by George A. Anastassiou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.
Current Topics In Summability Theory And Applications
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Author : Hemen Dutta
language : en
Publisher: Springer
Release Date : 2016-04-28
Current Topics In Summability Theory And Applications written by Hemen Dutta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Mathematics categories.
This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world. The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis. Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world.
Towards Intelligent Modeling Statistical Approximation Theory
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-06
Towards Intelligent Modeling Statistical Approximation Theory written by George A. Anastassiou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-06 with Technology & Engineering categories.
The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
Progress In Approximation Theory
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Author : Paul G. Nevai
language : en
Publisher:
Release Date : 1991
Progress In Approximation Theory written by Paul G. Nevai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Advances In Functional Analysis And Fixed Point Theory
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Author : Bipan Hazarika
language : en
Publisher: Springer Nature
Release Date :
Advances In Functional Analysis And Fixed Point Theory written by Bipan Hazarika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Recent Advances In Constructive Approximation Theory
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Author : Vijay Gupta
language : en
Publisher: Springer
Release Date : 2018-07-06
Recent Advances In Constructive Approximation Theory written by Vijay Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.
This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.
Progress In Approximation Theory
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Author : A.A. Gonchar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Progress In Approximation Theory written by A.A. Gonchar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.
Approximation Theory Sequence Spaces And Applications
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Author : S. A. Mohiuddine
language : en
Publisher: Springer Nature
Release Date : 2022-12-07
Approximation Theory Sequence Spaces And Applications written by S. A. Mohiuddine and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-07 with Mathematics categories.
This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
An Introductory Course In Summability Theory
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Author : Ants Aasma
language : en
Publisher: John Wiley & Sons
Release Date : 2017-04-05
An Introductory Course In Summability Theory written by Ants Aasma and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) - method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.