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Baskakov-Szász-type operators based on inverse Pólya-Eggenberger distribution. (English) Zbl 1354.41020

Summary: The present article deals with the modified forms of the Baskakov and Szász basis functions. We introduce a Durrmeyer-type operator having the basis functions in summation and integration due to D. D. Stancu [An. Univ. Timişoara, Ştiinţe Mat. 8, 213–220 (1970; Zbl 0276.41009)] and R. Păltănea [Carpathian J. Math. 24, No. 3, 378–385 (2008; Zbl 1249.41064)]. We obtain some approximation results, which include the Voronovskaja-type asymptotic formula, local approximation, error estimation in terms of the modulus of continuity, and weighted approximation. Also, the rate of convergence for functions with derivatives of bounded variation is established. Furthermore, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

MSC:

41A36 Approximation by positive operators
41A35 Approximation by operators (in particular, by integral operators)
41A25 Rate of convergence, degree of approximation

Software:

Maple
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