On the Generalized Baskakov Durrmeyer Operators

The intent of this article is to construct Baskakov Durrmeyer type operators. Their structure depends on a function τ. We exude the uniform convergence of the operators using the weighted modulus of continuity. Moreover we obtain pointwise convergence of ? ? ? ? by obtaining Voronovskaya type theorem.

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T. Acar, A. Aral and I. Raşa, "Modified Bernstein- Durrmeyer operators," General Mathematics, vol. 22, no. 1, pp. 27-41, 2014.

T. Acar, G. Ulusoy, "Approximation by modified Szasz Durrmeyer operators," Period Math Hung, vol. 72, pp. 64-75, 2016.

A. M. Acu, S. Hodiş and I. Raşa, "A Survey on Estimates for the Differences of Positive Linear Operators, " Constr. Math. Anal., vol. 1, no. 2, pp. 113- 127, 2018.

A. Aral, D. Inoan and I. Raşa, "On the Generalized Szász-Mirakyan Operators," Results in Mathematics, vol. 65, pp. 441-452, 2014.

V. Baskakov, "An instance of a sequence of linear positive operators in the space of continuous functions," Doklady Akademii Nauk SSSR, vol. 113, no. 2, pp. 249-251, 1957.

D. Cárdenas-Morales, P. Garrancho, I. Raşa, "Bernstein-type operators which preserve polynomials," Computers and Mathematics with Applications, vol. 62, pp. 158-163, 2011.

A. D. Gadziev, "The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogues to that of P. P. Korovkin," Dokl. Akad. Nauk SSSR, vol. 218, pp. 1001-1004, 1974. Also in Soviet Math Dokl. vol. 15, pp. 1433- 1436, 1974 (in English).

A. D. Gadziev, "Theorems of the type of P. P. Korovkin's theorems (in Russian)," Math. Z., vol. 205, pp. 781-786, 1976 translated in Math. Notes, vol. 20, no. 5-6, pp. 995-998, 1977.

A. Holhos, "Quantitative estimates for positive linear operators in weighted space," General Math., vol. 16, no. 4, pp. 99-110, 2008.

A. Kajla, "On the Bézier Variant of the Srivastava-Gupta Operators, " Constr. Math. Anal., vol. 1, no. 2, pp. 99-107, 2018.

Prashantkumar Patel, Vishnu Narayan Mishra and Mediha Örkcü, "Some approximation properties of the generalized Baskakov operators," Journal of Interdisciplinary Mathematics, vol. 21, no. 3, pp. 611- 622, 2018.