A Survey on Durrmeyer-Type Operators

Vijay Gupta (), Themistocles M. Rassias () and Jyoti Sinha ()
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Vijay Gupta: Netaji Subhas Institute of Technology, Department of Mathematics
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics
Jyoti Sinha: Inderprastha Engineering College, Department of Applied Mathematics

A chapter in Contributions in Mathematics and Engineering, 2016, pp 299-312 from Springer

Abstract: Abstract It is well known that discretely defined operators such as Bernstein polynomials, Baskakov operators, Szász–Mirakyan, Meyer-König–Zeller operators, Stancu operators, Jain operators, and their modified versions are not possible to approximate Lebesgue integrable functions. In the year 1930, Kantorovich proposed integral modification of the Bernstein polynomials. The more general integral modification of the Bernstein polynomial was given by Durrmeyer in the year 1967. After this several Durrmeyer-type modifications of different operators have been introduced and their approximation properties have been discussed. In the present note, to the best of our knowledge, we present the different Durrmeyer-type operators introduced in the last five decades. We also propose some open problems in the end.

Keywords: Durrmeyer-type Modification; Approximate Lebesgue Integrable Functions; Baskakov Operators; Bernstein Polynomials; Durrmeyer Variant (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31317-7_14

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