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Approximation by generalized Baskakov–Durrmeyer–Stancu type operators

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Abstract

In this paper, we introduce Stancu type modification of generalized Baskakov–Durrmeyer operators and study their approximation properties. First, we derive the recurrence relation and central moments of these operators and then we study the local approximation, weighted approximation results for the new operators. The last section is devoted to A-statistical convergence behaviours of these operators by using the Korovkin type approximation of statistical convergence.

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Acknowledgments

The authors are extremely grateful to the reviewer for a careful reading of the manuscript and making valuable suggestions leading to a better presentation of the paper.

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Authors and Affiliations

  1. School of Advanced Sciences, Department of Mathematics, VIT University, Chennai Campus, Chennai, 600127, India

    A. Sathish Kumar

  2. Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450, Yahsihan, Kirikkale, Turkey

    Tuncer Acar

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  1. A. Sathish Kumar
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  2. Tuncer Acar
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Correspondence to A. Sathish Kumar.

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Kumar, A.S., Acar, T. Approximation by generalized Baskakov–Durrmeyer–Stancu type operators. Rend. Circ. Mat. Palermo, II. Ser 65, 411–424 (2016). https://doi.org/10.1007/s12215-016-0242-1

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  • DOI: https://doi.org/10.1007/s12215-016-0242-1

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