Approximation by complex Bernstein and convolution type operators:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore
World Scientific Pub. Co.
©2009
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| Schriftenreihe: | Series on concrete and applicable mathematics
v. 8 |
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002 Includes bibliographical references (pages 327-336) and index 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 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 |
| Beschreibung: | 1 Online-Ressource (xii, 337 pages) |
| ISBN: | 9789814282420 9789814282437 9814282421 981428243X |
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| 500 | |a Includes bibliographical references (pages 327-336) and index | ||
| 500 | |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 | ||
| 500 | |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 | 4 | |a Bernstein polynomials | |
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Datensatz im Suchindex
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| author | Gal, Sorin G. |
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| dewey-full | 511.4 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043126290 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:14Z |
| institution | BVB |
| isbn | 9789814282420 9789814282437 9814282421 981428243X |
| language | English |
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| publishDate | 2009 |
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| spelling | Gal, Sorin G. Verfasser aut Approximation by complex Bernstein and convolution type operators Sorin G. Gal Singapore World Scientific Pub. Co. ©2009 1 Online-Ressource (xii, 337 pages) txt rdacontent c rdamedia cr rdacarrier Series on concrete and applicable mathematics v. 8 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002 Includes bibliographical references (pages 327-336) and index 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 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 MATHEMATICS / General bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340525 Aggregator Volltext |
| spellingShingle | Gal, Sorin G. Approximation by complex Bernstein and convolution type operators MATHEMATICS / General bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) |
| title | Approximation by complex Bernstein and convolution type operators |
| title_auth | Approximation by complex Bernstein and convolution type operators |
| title_exact_search | Approximation by complex Bernstein and convolution type operators |
| title_full | Approximation by complex Bernstein and convolution type operators Sorin G. Gal |
| title_fullStr | Approximation by complex Bernstein and convolution type operators Sorin G. Gal |
| title_full_unstemmed | Approximation by complex Bernstein and convolution type operators Sorin G. Gal |
| title_short | Approximation by complex Bernstein and convolution type operators |
| title_sort | approximation by complex bernstein and convolution type operators |
| topic | MATHEMATICS / General bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) |
| topic_facet | MATHEMATICS / General Approximation theory Bernstein polynomials Convolutions (Mathematics) Operator theory |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340525 |
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