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On Approximation Properties of Szász–Mirakyan Operators

In: Handbook of Functional Equations

Author

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  • Vijay Gupta

    (Netaji Subhas Institute of Technology)

Abstract

In the present chapter, we present approximation properties of the well-known Szász-Mirakyan operators. These operators were introduced in the middle of last century and because of their important properties, researchers continued to work on such operators and their different modifications. Although there are several modifications of the Szász-Mirakyan operators available in the literature viz. integral modifications due to Kantorovich, Durrmeyer and mixed operators, but here we discuss only the discrete modifications of these operators which were proposed by several researchers in last 60 years. In the recent years, overconvergence properties were studied by considering the complex version of Szász-Mirakyan operators. In the last section, we consider complex Szász-Stancu operators and establish upper bound and a Voronovskaja type result with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks.

Suggested Citation

  • Vijay Gupta, 2014. "On Approximation Properties of Szász–Mirakyan Operators," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 247-271, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1246-9_11
    DOI: 10.1007/978-1-4939-1246-9_11
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