04274nam 2200685 a 450 991082406910332120240404143101.01-282-76138-29786612761386981-4282-43-X(CKB)2490000000001623(EBL)1679536(OCoLC)612412955(SSID)ssj0000412023(PQKBManifestationID)12110368(PQKBTitleCode)TC0000412023(PQKBWorkID)10365601(PQKB)10293286(MiAaPQ)EBC1679536(WSP)00000584 (Au-PeEL)EBL1679536(CaPaEBR)ebr10422512(CaONFJC)MIL276138(EXLCZ)99249000000000162320091120d2009 uy 0engur|n|---|||||txtccrApproximation by complex Bernstein and convolution type operators /Sorin G. Gal1st ed.Singapore ;Hackensack, N.J. World Scientificc20091 online resource (350 p.)Series on concrete and applicable mathematics,1793-1142 ;v. 8Description based upon print version of record.981-4282-42-1 Includes bibliographical references (p. 327-336) and index.Contents; Preface; 1. Bernstein-Type Operators of One Complex Variable; 1.0 Auxiliary Results in Complex Analysis; 1.1 Bernstein Polynomials; 1.1.1 Bernstein Polynomials on Compact Disks; 1.1.2 Bernstein-Faber Polynomials on Compact Sets; 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-Sz asz-Mirakjan Operators; 1.9 Baskakov Operators1.10 Bal azs-Szabados Operators1.11 Bibliographical Notes and Open Problems; 2. Bernstein-Type Operators of Several Complex Variables; 2.1 Introduction; 2.2 Bernstein Polynomials; 2.3 Favard-Sz asz-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; 3.2.1 Picard, Poisson-Cauchy and Gauss-Weierstrass Complex Convolutions; 3.2.2 Complex q-Picard and q-Gauss-Weierstrass Singular Integrals; 3.2.3 Post-Widder Complex Convolution3.2.4 Rotation-Invariant Complex Convolutions3.2.5 Sikkema Complex Convolutions; 3.3 Nonlinear Complex Convolutions; 3.4 Bibliographical Notes and Open Problems; 4. Appendix : Related Topics; 4.1 Bernstein Polynomials of Quaternion Variable; 4.2 Approximation of Vector-Valued Functions; 4.2.1 Real Variable Case; 4.2.2 Complex Variable Case; 4.3 Strong Approximation by Complex Taylor Series; 4.4 Bibliographical Notes and Open Problems; Bibliography; Index 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, <i>q</i>-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 properSeries on concrete and applicable mathematics ;v. 8.Approximation theoryOperator theoryBernstein polynomialsConvolutions (Mathematics)Approximation theory.Operator theory.Bernstein polynomials.Convolutions (Mathematics)511/.4Gal Sorin G.1953-474332MiAaPQMiAaPQMiAaPQBOOK9910824069103321Approximation by complex Bernstein and convolution type operators3987114UNINA