Name: Approximation Theory Using Positive Linear Operators By Radu Paltanea
SKU: 9780817643508
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Approximation Theory Using Positive Linear Operators Summary

Approximation Theory Using Positive Linear Operators by Radu Paltanea

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

Approximation Theory Using Positive Linear Operators Reviews

From the reviews:

This monograph will be of interest to those working in the field of approximation, and it may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject.(ZENTRALBLATT MATH)

1 Introduction.- 1.1 Operators and functionals. Moduli of continuity.- 1.2 Approximation of functions by sequences of positive linear operators.- 1.2.1 Basic theorems of convergence.- 1.2.2 Estimates with the first order modulus.- 2 Estimates with Second Order Moduli.- 2.1 A general approach.- 2.1.1 Introduction.- 2.1.2 A general estimate for the degree of approximation by linear positive functionals.- 2.2 Estimates with moduli ?2? and ?2?.- 2.2.1 Introduction. Auxiliary results.- 2.2.2 Main results.- 2.3 Estimates with modulus ?2d.- 2.3.1 Introduction. Auxiliary results.- 2.3.2 Main results.- 2.4 Estimates with modulus ?2dd.- 2.5 Estimates with DitzianTotik modulus.- 2.5.1 Auxiliary results.- 2.5.2 Main result.- 3 Absolute Optimal Constants.- 3.1 Introduction.- 3.2 Discrete functionals and the classical second order modulus ?2.- 3.3 General functionals and the second order modulus with parameter ?2?.- 3.3.1 A particular case.- 3.3.2 The main results.- 4 Estimates for the Bernstein Operators.- 4.1 Various types of estimates.- 4.1.1 Introduction.- 4.1.2 Applications of general estimates.- 4.2 Best constant in the estimate with modulus ?2.- 4.2.1 Introduction. Main result.- 4.2.2 Proof of the direct part of the theorem for n ? 60.- 4.2.3 Proof of the direct part of the theorem for 1 ? n ? 59.- 4.3 Global smoothness preservation.- 5 Two Classes of Bernstein Type Operators.- 5.1 Generalized Brass type operators.- 5.1.1 Definitions and general properties.- 5.1.2 Simultaneous approximation.- 5.2 Generalized Durrmeyer type operators.- 5.2.1 Durrmeyer type operators with general weights.- 5.2.2 Durrmeyer type operators with generalized Jacobi weights.- 6 Approximation Operators for Vector-Valued Functions.- 6.1 Approximation of functions with real argument.- 6.1.1 Introduction. Generalized positive and convex operators.- 6.1.2 A Korovkin type theorem.- 6.1.3 Simultaneous approximation.- 6.2 Approximation of functions with vector argument.- 6.2.1 Introduction. Linear functionals and operators induced by positive measures.- 6.2.2 Auxilliary results.- 6.2.3 Estimates with moduli ?2 and ?2?.- 6.2.4 Estimates with modulus $$ {{\tilde{\omega }}_{2}} $$.- References.

Additional information

Sku

NPB9780817643508

ISBN 13

9780817643508

ISBN 10

0817643508

Title

Approximation Theory Using Positive Linear Operators by Radu Paltanea

Author

Radu Paltanea

Condition

New

Binding type

Paperback

Publisher

Birkhauser Boston Inc

Year published

2004-09-17

Number of pages

202

Prizes

N/A

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Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

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This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Approximation Theory Using Positive Linear Operators Radu Paltanea

Approximation Theory Using Positive Linear Operators by Radu Paltanea

Summary

Approximation Theory Using Positive Linear Operators Summary

Approximation Theory Using Positive Linear Operators by Radu Paltanea

Approximation Theory Using Positive Linear Operators Reviews

Table of Contents

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Customer Reviews - Approximation Theory Using Positive Linear Operators