Approximation by Complex Durrmeyer Type Operators in Compact Disks

S. G. Gal () and Vijay Gupta ()
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S. G. Gal: University of Oradea, Department of Mathematics and Computer Science
Vijay Gupta: School of Applied Sciences, Netaji Subhas Institute of Technology

A chapter in Mathematics Without Boundaries, 2014, pp 263-285 from Springer

Abstract: 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.

Keywords: Complex durrmeyer operators; Voronovskaja type result; Exact order; Compact disk (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1124-0_9

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DOI: 10.1007/978-1-4939-1124-0_9

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