LEADER 04277nam 2200673 a 450 001 9910780725903321 005 20230721024423.0 010 $a1-282-76138-2 010 $a9786612761386 010 $a981-4282-43-X 035 $a(CKB)2490000000001623 035 $a(EBL)1679536 035 $a(OCoLC)612412955 035 $a(SSID)ssj0000412023 035 $a(PQKBManifestationID)12110368 035 $a(PQKBTitleCode)TC0000412023 035 $a(PQKBWorkID)10365601 035 $a(PQKB)10293286 035 $a(MiAaPQ)EBC1679536 035 $a(WSP)00000584 035 $a(Au-PeEL)EBL1679536 035 $a(CaPaEBR)ebr10422512 035 $a(CaONFJC)MIL276138 035 $a(EXLCZ)992490000000001623 100 $a20091120d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApproximation by complex Bernstein and convolution type operators$b[electronic resource] /$fSorin G. Gal 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2009 215 $a1 online resource (350 p.) 225 1 $aSeries on concrete and applicable mathematics,$x1793-1142 ;$vv. 8 300 $aDescription based upon print version of record. 311 $a981-4282-42-1 320 $aIncludes bibliographical references (p. 327-336) and index. 327 $aContents; 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 Operators 327 $a1.10 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 Convolution 327 $a3.2.4 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 330 $a The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Sza?sz-Mirakjan, Baskakov and Bala?zs-Szabados. The second main objective is to provide a study of the approximation and geometric proper 410 0$aSeries on concrete and applicable mathematics ;$vv. 8. 606 $aApproximation theory 606 $aOperator theory 606 $aBernstein polynomials 606 $aConvolutions (Mathematics) 615 0$aApproximation theory. 615 0$aOperator theory. 615 0$aBernstein polynomials. 615 0$aConvolutions (Mathematics) 676 $a511/.4 700 $aGal$b Sorin G.$f1953-$0474332 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780725903321 996 $aApproximation by complex Bernstein and convolution type operators$93758138 997 $aUNINA