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Approximation by complex Bernstein and convolution type operators /

The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. T...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Gal, Sorin G., 1953-
Autor Corporativo: World Scientific (Firm)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2009.
Colección:Series on concrete and applicable mathematics ; v. 8.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Gal, Sorin G.,  |d 1953-  |1 https://id.oclc.org/worldcat/entity/E39PCjxmpxDQH799yTC9rc6R8C 
245 1 0 |a Approximation by complex Bernstein and convolution type operators /  |c Sorin G. Gal. 
260 |a Singapore ;  |a Hackensack, N.J. :  |b World Scientific Pub. Co.,  |c ©2009. 
300 |a 1 online resource (xii, 337 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a data file 
490 1 |a Series on concrete and applicable mathematics,  |x 1793-1142 ;  |v v. 8 
504 |a Includes bibliographical references (pages 327-336) and index. 
505 0 |a 1. Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. Bibliographical notes and open problems. 
520 |a The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types : Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions : the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions. 
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650 0 |a Approximation theory. 
650 0 |a Operator theory. 
650 0 |a Bernstein polynomials. 
650 0 |a Convolutions (Mathematics) 
650 6 |a Théorie de l'approximation. 
650 6 |a Théorie des opérateurs. 
650 6 |a Polynômes de Bernstein. 
650 6 |a Convolutions (Mathématiques) 
650 7 |a MATHEMATICS  |x General.  |2 bisacsh 
650 7 |a Approximation theory  |2 fast 
650 7 |a Bernstein polynomials  |2 fast 
650 7 |a Convolutions (Mathematics)  |2 fast 
650 7 |a Operator theory  |2 fast 
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