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Approximation by Lupas-type operators and Szász-Mirakyan-type operators. (English) Zbl 1247.41013

Summary: Lupas-type operators and Szász-Mirakyan-type operators are the modifications of Bernstein polynomials to infinite intervals. We investigate the convergence of Lupas-type operators and Szász-Mirakyan-type operators on \([0, \infty)\).

MSC:

41A35 Approximation by operators (in particular, by integral operators)
41A36 Approximation by positive operators
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References:

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[2] A. Sahai and G. Prasad, “On simultaneous approximation by modified Lupas operators,” Journal of Approximation Theory, vol. 45, no. 2, pp. 122-128, 1985. · Zbl 0596.41035
[3] L. Rempulska and S. Graczyk, “On certain class of Szász-Mirakyan operators in exponential weight spaces,” International Journal of Pure and Applied Mathematics, vol. 60, no. 3, pp. 259-267, 2010. · Zbl 1196.41015
[4] M. Becker, D. Kucharski, and R. J. Nessel, “Global approximation theorems for the Szász-Mirakjan operators in exponential weight spaces,” in Linear Spaces and Approximation, pp. 319-333, Birkhäuser, Basle, Switzerland, 1978. · Zbl 0386.41014
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