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Approximation by Complex Durrmeyer Type Operators in Compact Disks

In: Mathematics Without Boundaries

Author

Listed:
  • S. G. Gal

    (University of Oradea, Department of Mathematics and Computer Science)

  • Vijay Gupta

    (School of Applied Sciences, Netaji Subhas Institute of Technology)

Abstract

A general family of Durrmeyer type operators was proposed in Srivastava and Gupta (Math Comput Model 37(12–13):1307–1315, 2003). As important particular cases, we can mention the Bernstein–Durrmeyer type operators, the Szász–Durrmeyer type operators (including the subcase of the Phillips operators) and the Baskakov–Durrmeyer type operators, whose approximation properties in real intervals were intensively studied by several researchers. The goal of the present work is to present approximation properties in complex domains for most of these operators. For analytic functions in compact disks, we establish Voronovskaja type results with quantitative estimates and the exact order in the simultaneous approximation is found. The results in the case of the complex Phillips operators are new and appear for the first time here.

Suggested Citation

  • S. G. Gal & Vijay Gupta, 2014. "Approximation by Complex Durrmeyer Type Operators in Compact Disks," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Mathematics Without Boundaries, edition 127, pages 263-285, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1124-0_9
    DOI: 10.1007/978-1-4939-1124-0_9
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