The Complete Asymptotic Expansion for the Left Quasi Interpolants of Müller's Gamma Operators

References

• Abel , U. 1997 . The complete asymptotic expansion for the Meyer-König and Zeller operators . J. Math. Anal. Appl. , 208 : 109 – 119 .
   Web of Science ®Google Scholar
• Abel , U. and Ivan , M. 2003 . Asymptotic approximation of functions and their derivatives by Müller's Gamma operators . Results Math. , 43 : 1 – 12 .
   Google Scholar
• Comtet , L. 1974 . Advanced Combinatorics Dordrecht : Reidel Publishing Comp .
   Google Scholar
• Jordan , C. 1965 . Calculus of finite differences New York : Chelsea .
   Google Scholar
• Kageyama , Y. 1998 . Generalization of the left Bernstein quasi-interpolants . J. Approx. Theory , 94 : 306 – 329 .
   Web of Science ®Google Scholar
• Kageyama , Y. 1999 . A new class of modified Bernstein operators . J. Approx. Theory , 101 : 121 – 147 .
   Web of Science ®Google Scholar
• Lupaş , A. and Müller , M. W. 1967 . Approximationseigenschaften der Gamma-operatoren . Math. Zeitschr. , 98 : 208 – 226 .
   Web of Science ®Google Scholar
• Lupaş , A. , Mache , D. H. , Maier , V. and Müller , M. W. 1998 . Linear combinations of Gammaoperators in L p spaces . Results Math. , 34 : 156 – 168 .
   Google Scholar
• Lupaş , A. , Mache , D. H. and Müller , M. W. 1995 . Weighted L p approximation of derivatives by the method of Gammaoperators . Results Math. , 28 : 277 – 286 .
   Google Scholar
• Mache , P. and Mache , D. H. 2001 . Approximation by Bernstein quasi-interpolants . Numer. Funct. Anal. Optimization , 22 : 159 – 175 .
   Web of Science ®Google Scholar
• Müller , M. W. 1967 . Die Folge der Gammaoperatoren Stuttgart : Dissertation .
   Google Scholar
• Müller , M. W. 1968 . Punktweise und gleichmässige Approximation durch Gammaoperatoren . Math. Zeitschr. , 103 : 227 – 238 .
   Web of Science ®Google Scholar
• Müller , M. W. 2001 . The central approximation theorems for the method of left gamma quasi-interpolants in L p spaces . J. Comp. Anal. Appl. , 3 : 207 – 222 .
   Web of Science ®Google Scholar
• Reif , B. 1994 . Asymptotische Approximation durch die Operatoren von Meyer-König und Zeller Fachhochschule Giessen-Friedberg . Diploma thesis
   Google Scholar
• Sablonnière , P. 1998 . “ Representation of quasi-interpolants as differential operators and applications ” . In New Developments in Approximation Theory , International Series of Numerical Mathematics Edited by: Müller , M. W. , Buhmann , M. , Mache , D. H. and Felten , M. Vol. 132 , pp. 233 – 253 . Basel : Birkhäuser-Verlag .
   Google Scholar
• Sikkema , P. C. 1970a . On some linear positive operators . Indag. Math. , 32 : 327 – 337 .
   Google Scholar
• Sikkema , P. C. 1970b . On the asymptotic approximation with operators of Meyer-König and Zeller . Indag. Math. , 32 : 428 – 440 .
   Google Scholar
• Totik , V. 1985 . The gammaoperators in L p spaces. . Publ. Math. Debrecen , 32 : 43 – 55 .
   Web of Science ®Google Scholar