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Approximation for Generalization of Baskakov–Durrmeyer Operators

In: Mathematical Analysis, Approximation Theory and Their Applications

Author

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  • Vijay Gupta

    (Netaji Subhas Institute of Technology)

Abstract

In the present article, we study certain approximation properties of the modified form of generalized Baskakov operators introduced by Erencin (Appl. Math. Comput. 218(3):4384–4390, 2011). We estimate a recurrence relation for the moments of their Durrmeyer type modification. First we estimate rate of convergence for functions having derivatives of bounded variation. Next, we discuss some direct results in simultaneous approximation by these operators, e.g. point-wise convergence theorem, Voronovskaja-type theorem and an estimate of error in terms of the modulus of continuity.

Suggested Citation

  • Vijay Gupta, 2016. "Approximation for Generalization of Baskakov–Durrmeyer Operators," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 317-338, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31281-1_14
    DOI: 10.1007/978-3-319-31281-1_14
    as

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