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Operators of Durrmeyer Type with Respect to Arbitrary Measure

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

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Abstract

In this paper, we give an overview of operators of Durrmeyer type with respect to arbitrary measure. Our construction includes the Bernstein–Durrmeyer operator, the Szász–Mirakjan–Durrmeyer operator, and the Baskakov–Durrmeyer operator with respect to arbitrary measure. We are particularly interested in the convergence of the operators. We discuss the uniform and the pointwise convergence as well as convergence in the corresponding weighted \(L^p\)-spaces. A new result is the statement on the \(L^p\)-convergence of the Szász–Mirakjan–Durrmeyer operator and the Baskakov–Durrmeyer operator without additional restrictions on the measure.

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Authors and Affiliations

  1. Department of Mathematics and Science, German University of Technology in Oman, PC 130 Athaibah, P.O. Box 1816, Muscat, Sultanate of Oman

    Elena E. Berdysheva

Authors
  1. Elena E. Berdysheva
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Correspondence to Elena E. Berdysheva .

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Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Berdysheva, E.E. (2015). Operators of Durrmeyer Type with Respect to Arbitrary Measure. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_20

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