Title Convergence Estimates in Approximation Theory / Vijay Gupta, Ravi P. Agarwal

Published Wien : Springer, [2014] ©2014

Table of Contents
1.	Preliminaries					1
1.1.	Korovkin's Theorem					2
1.2.	Weierstrass Approximation Theorems					4
1.3.	Order of Approximation					8
1.4.	Differential Properties of Function					11
1.5.	Notations and Inequalities					13
1.6.	Bounded Variation					15
2.	Approximation by Certain Operators					17
2.1.	Discretely Defined Operators					17
2.2.	Kantorovich Operators					27
2.3.	Durrmeyer-Type Operators					29
2.4.	Szász-Beta-Type Operators					36
2.5.	Phillips Operators					52
2.6.	Integral Modification of Jain Operators					60
2.7.	Generalized Bernstein-Durrmeyer Operators					64
2.8.	Generalizations of Baskakov Operators					72
2.9.	Mixed Summation-Integral Operators					89
3.	Complete Asymptotic Expansion					93
3.1.	Baskakov-Kantorovich Operators					93
3.2.	Baskakov-Szász-Durrmeyer Operators					97
3.3.	Meyer-König-Zeller-Durrmeyer Operators					100
3.4.	Beta Operators of the First Kind					103
4.	Linear and Iterative Combinations					109
4.1.	Linear Combinations					109
4.2.	Iterative Combinations					118
4.3.	Another Form of Linear Combinations					129
4.4.	Combinations of Szász-Baskakov Operators					132
5.	Better Approximation					141
5.1.	Bernstein-Durrmeyer-Type Operators					142
5.2.	Phillips Operators					146
5.3.	Szász-Mirakjan-Beta Operators					147
5.4.	Integrated Szász-Mirakjan Operators					149
5.5.	Beta Operators of the Second Kind					151
6.	Complex Operators in Compact Disks					155
6.1.	Complex Baskakov-Stancu Operators					155
6.2.	Complex Favard-Szász-Mirakjan-Stancu Operators					166
6.3.	Complex Beta Operators of the Second Kind					175
6.4.	Genuine Durrmeyer-Stancu Polynomials					189
6.5.	New Complex Durrmeyer Operators					196
6.6.	Complex q-Durrmeyer-Type Operators					206
6.7.	Complex q-Bernstein-Schurer Operators					210
7.	Rate of Convergence for Functions of Bounded Variation					213
7.1.	Fourier and Fourier-Legendre Series					213
7.2.	Hermite-Fejér Polynomials					216
7.3.	Exponential-Type Operators					217
7.4.	Bernstein-Durrmeyer-Type Polynomials					222
7.5.	Szász-Mirakyan-Durrmeyer-Type Operators					226
7.6.	Baskakov-Durrmeyer-Type Operators					231
7.7.	Baskakov-Beta Operators					239
7.8.	General Summation-Integral-Type Operators					242
7.9.	Meyer-König-Zeller Operators					244
8.	Convergence for Bounded Functions on Bézier Variants					249
8.1.	Bernstein-Bézier-Type Operators					250
8.2.	Bleimann-Butzer-Hann-Bézier Operators					252
8.3.	Balazs-Kantorovich-Bézier Operators					254
8.4.	Szász-Kantorovich-Bézier Operators					257
8.5.	Baskakov-Bézier Operators					264
8.6.	Baskakov-Kantorovich-Bézier Operators					268
8.7.	Baskakov-Durrmeyer-Bézier Operators					275
8.8.	MKZ Bézier-Type Operators					280
9.	Some More Results on the Rate of Convergence					287
9.1.	Nonlinear Operators					287
9.2.	Chanturiya's Modulus of Variation					296
9.3.	Functions with Derivatives of Bounded Variation					301
9.4.	Convergence for Bounded and Absolutely Continuous Functions					308
10.	Rate of Convergence in Simultaneous Approximation					313
10.1.	Bernstein-Durrmeyer-Bézier-Type Operators					314
10.2.	General Class of Operators for DBV					325
10.3.	Baskakov-Beta Operators for DBV					333
10.4.	Szász-Mirakian-Stancu-Durrmeyer Operators					334
11.	Future Scope and Open Problems					345
	References					349
	Index					359

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Description 1 online resource (308 pages) Contents 1. Preliminaries -- 2. Approximation by Certain Operators -- 3. Complete Asymptotic Expansion -- 4. Linear and Iterative Combinations -- 5. Better Approximation -- 6. Complex Operators in Compact Disks -- 7. Rate of Convergence for Functions of BV -- 8. Convergence for BV/Bounded Functions on Bezier Variants -- 9. Some More Results on Rate of Convergence -- 10. Rate of Convergence in Simultaneous Approximation -- 11. Future Scope and Open Problems Summary The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches Notes Print version record Subject Approximation theory. MATHEMATICS -- General. Approximation theory Form Electronic book Author Agarwal, Ravi P., author. ISBN 9783319027654 3319027654

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