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On The Asymptotic Behaviour And Smoothness Properties Of Some Positive Linear Operators For The Approximation Of Continuous Functions
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Book Synopsis On the Asymptotic Behaviour and Smoothness Properties of Some Positive Linear Operators for the Approximation of Continuous Functions by :
Download or read book On the Asymptotic Behaviour and Smoothness Properties of Some Positive Linear Operators for the Approximation of Continuous Functions written by and published by . This book was released on 1972 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Approximation of Continuous Functions by Positive Linear Operators by : Ronald A. DeVore
Download or read book The Approximation of Continuous Functions by Positive Linear Operators written by Ronald A. DeVore and published by Springer. This book was released on 1972-01-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Approximation of Continuous Functions by Positive Linear Operators by : Ronald A. De Vore
Download or read book The Approximation of Continuous Functions by Positive Linear Operators written by Ronald A. De Vore and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Operators, Positive Semigroups and Approximation Processes by : Francesco Altomare
Download or read book Markov Operators, Positive Semigroups and Approximation Processes written by Francesco Altomare and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-12-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.
Book Synopsis Quantitative Estimates for Certain Positive Linear Operators by : Gunjan Agarwal
Download or read book Quantitative Estimates for Certain Positive Linear Operators written by Gunjan Agarwal and published by . This book was released on 2024-01-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The convergence behaviour of linear positive operators has been a prominent topic and many scholars have investigated it using a variety of methodologies for exactness. Approx- imation theory is primarily concerned with the investigation of several direct results such as the asymptotic formula, point-wise convergence and error estimates in simultaneous and ordinary approximation. These findings are necessary from a convergence standpoint. Dun- ham Jackson [103] proved algebraic and trigonometric polynomial direct theorems. Profes- sor Edmund Georg Hermann Landau, Jackson's supervisor, was the one who came up with the Big-O and small-o symbols. The asymptotic behaviour of a function is represented by these symbols. Because a function's rate of growth is known as its order, the letter 'O' or 'o' is utilised. As a result, the order of approximation is represented by these symbols. The crucial theorem proved by Weierstrass in 1885 made it possible to study some sorts of complicated functions by a simpler function with a suitable rate of approximation. Thus, linear positive operator approximation theory is based mostly on the "Weierstrass approxima- tion theorem," which states that "every continuous function defined on a closed and bounded interval may be uniformly approximated by a polynomial". Polynomials are among the most basic functions and computers can instantly evaluate polynomials. The Bernstein polyno- mials are used in the most typical proof of this well-known theorem. Additionally, Borislav Dechev Boyanov [33] was one of the pioneers in the field of mathematics to demonstrate the presence and originality of answers to numerous issues pertaining to approximation the- ory. Academician Blagovest Hristov Sendov, who served as his supervisor, visited Moscow State University in the early 1960s as new, interesting fields in approximation theory began to emerge. During this time, Sergei Natanovich Bernstein was still engaged in mathematical studies.
Book Synopsis On Asymptotic Approximation by Some Positive Linear Operators by : Santosh Kumar Sinha
Download or read book On Asymptotic Approximation by Some Positive Linear Operators written by Santosh Kumar Sinha and published by . This book was released on 2016-10-24 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the degree of approximation of continuous functions by positive linear operators by : Jovan Karamata
Download or read book On the degree of approximation of continuous functions by positive linear operators written by Jovan Karamata and published by . This book was released on 1964 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theorem of B. Bajsanski and R. Bojanic ('A note on approximation by Bernstein polynomials.' Bull. Amer. Math. Soc. 70(1964), p. 675-677) is extended to general linear positive operators. (Author).
Book Synopsis The Approximation of Continuous Functions by Positive Linear Operators by : Ronald A. DeVore
Download or read book The Approximation of Continuous Functions by Positive Linear Operators written by Ronald A. DeVore and published by . This book was released on 1972 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators by : Nira Dyn
Download or read book Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators written by Nira Dyn and published by World Scientific. This book was released on 2014-10-30 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
Book Synopsis Evolutionary Equations with Applications in Natural Sciences by : Jacek Banasiak
Download or read book Evolutionary Equations with Applications in Natural Sciences written by Jacek Banasiak and published by Springer. This book was released on 2014-11-07 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximation with Positive Linear Operators and Linear Combinations by : Vijay Gupta
Download or read book Approximation with Positive Linear Operators and Linear Combinations written by Vijay Gupta and published by Springer. This book was released on 2018-08-02 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Book Synopsis Linear Operators and Approximation Theory by : Pavel Petrovich Korovkin
Download or read book Linear Operators and Approximation Theory written by Pavel Petrovich Korovkin and published by . This book was released on 1960 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximation of Functions and Operators by : S. B. Stechkin
Download or read book Approximation of Functions and Operators written by S. B. Stechkin and published by American Mathematical Soc.. This book was released on 1977 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about approximation theory.
Book Synopsis Algebraic Approximation: A Guide to Past and Current Solutions by : Jorge Bustamante
Download or read book Algebraic Approximation: A Guide to Past and Current Solutions written by Jorge Bustamante and published by Springer Science & Business Media. This book was released on 2011-11-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.
Book Synopsis On Positive Linear Operators by : Farzaneh Jannat
Download or read book On Positive Linear Operators written by Farzaneh Jannat and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation theory received much attention in the last century, and an intriguing area in this field is positive linear operators. This thesis is a literature survey on positive linear operators. We discuss some of the well-known examples of positive linear operators. Preserving $k$-monotonicity by positive linear operators is another interesting topic in this area. We are interested if $L_n(f;x)$ is $k$-monotone whenever function $f$ is $k$-monotone. For a sequence of positive linear operators $\{L_n(f;x)\}$, it is a natural question if this sequence converges to $f(x)$ and how fast is this convergence. We study the saturation of these operators. Usually, there is a relation between the rate of convergence and the smoothness of the function being approximated. If increasing smoothness of functions does not result in the increase of the degree of approximation, this phenomenon is called saturation. We discuss iteration of general positive linear operators and give numerical examples.
Book Synopsis Asymptotic Behavior of Generalized Functions by : Stevan Pilipovic
Download or read book Asymptotic Behavior of Generalized Functions written by Stevan Pilipovic and published by World Scientific. This book was released on 2012 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.
