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Author: Vijay Gupta
Publisher: Springer
ISBN: 3319587951
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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.
Author: Vijay Gupta
Publisher: Springer
ISBN: 3319587951
Category : Mathematics
Languages : en
Pages : 193
Get Book Here
Book Description
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.
Author: Radu Paltanea
Publisher: Springer Science & Business Media
ISBN: 1461220580
Category : Mathematics
Languages : en
Pages : 208
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Book Description
Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results
Author: Ronald A. De Vore
Publisher: Springer
ISBN: 3540379959
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Author: Ronald A. De Vore
Publisher:
ISBN: 9783662179765
Category :
Languages : en
Pages : 304
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Book Description
Author: Paula Piţul
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Jia-Ding Cao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Vijay Gupta
Publisher: Springer
ISBN: 3030194558
Category : Mathematics
Languages : en
Pages : 96
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Book Description
This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.
Author: Jia-Ding Cao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: S. A. Mohiuddine
Publisher: Springer Nature
ISBN: 9811961166
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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.
Author: S. A. Mohiuddine
Publisher: Springer
ISBN: 9811330778
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
