On Approximation Properties of Szász–Mirakyan Operators

Vijay Gupta ()
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Vijay Gupta: Netaji Subhas Institute of Technology

A chapter in Handbook of Functional Equations, 2014, pp 247-271 from Springer

Abstract: 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.

Keywords: Bernstein polynomials; Divided differences; Linear combinations; Asymptotic expansion; Rate of convergence; q integer ⋅ (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_11

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DOI: 10.1007/978-1-4939-1246-9_11

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