A Voronovskaja-Type Theorem for a Kind of Durrmeyer-Bernstein-Stancu Operators
A Voronovskaja-Type Theorem for a Kind of Durrmeyer-Bernstein-Stancu Operators
In this paper, we study on a Durrmeyer variant of Bernstein-Stancu operators. We give a Voronovskaja-type theorem for these type operators.
___
- [1] Bernstein, S. N., “Demonstration du theoreme de Weierstrass fondee sur le calcul de probabilities”, Commun. Soc. Math. Kharkow, 13(2): 1-2, (1912).
- [2] Durrmeyer, J. L., “Une Formule D’inversion de la transformée de Laplace: Aplications a la théorie des moments, Thése de 3e cycle”, Faculté des Sciences de I’Université de Paris, (1967).
- [3] Gadhziev, A. D. and Chorbanalizadeh, A. M., “Approximation properties of a new type BernsteinStancu polynomials of one and two variables”, Appl. Math. Comput., 216: 890-901, (2010).
- [4] Stancu, D. D., “Approximation of functions by a new class of linear polynomial operators”, Rev. Roum. Math. Pures Appl., 13: 1173-1194, (1968).
- [5] Dong, L. X. and Yu, D. S., “Pointwise Approximation by a Durrmeyer Variant of Bernstein-Stancu Operators”, J. Inequal Appl., 2017, 28, (2017).
- [6] Gadhziev, A. D., “Theorems of the type of P.P. Korovkin type theorems”, Math. Zametki, 20(5): 781786, (1976). (English Translation, Math. Notes, 20(5/6): 996-998, (1976).
- [7] Gupta, V. and Duman, O., “Bernstein–Durrmeyer type operators preserving linear function”, Matematicki Vesnik, 62(4): 259-264, (2010).
- [8] Tasdelen, F., Bascanbaz-Tunca, G. and Erencin, A., “On a new type Bernstein-Stancu operators”, Fasc. Math., 48: 119-128, (2012).
- [9] Acar, T., Aral, A. and Gupta, V., “On approximation properties of a new type Bernstein-Durrmeyer operators”, Math. Slovaca., 65: 1107-1122, (2015).
- [10] Icoz, G., “A Kantorovich variant of a new type Bernstein Stancu polynomials”, Appl. Math. Comput., 218: 8552-8560, (2012).
- [11] Wang, M. L., Yu, D. S. and Zhou, P., “On the approximation by operators of Bernstein-Stancu types”, Appl. Math. Comput., 246: 79-87, (2014).