A Voronovskaja-Type Theorem for a Kind of Durrmeyer-Bernstein-Stancu Operators

Abstract

In this paper, we study on a Durrmeyer variant of Bernstein-Stancu operators.  We give a Voronovskaja-type theorem for these type operators. 

Keywords

• Durrmeyer type operators,Bernstein-Stancu type operators,Voronovskaja type theorem

References

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 Bernstein-Stancu 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. and Yu D. “Pointwise Approximation By A Durrmeyer Variant Of Bernstein-Stancu Operators”. Jaurnal of ınequalities and applications , 2017:28 (2017)
6. Gadhziev, A.D. “Theorems of the type of P.P. Korovkin type theorems”. Math. Zametki 20 (5) (1976) 781-786 (English Translation, Math . Notes, 20 (5/6), 996-998 (1976)
7. Gupta V. and Duman O. “Bernstein – Durrmeyer type operators preserving linear function”. Matematikci Vesnik 62(4) 259-264 (2010)
8. Taşdelen, F., Başcanbaz-Tunca G. and Erençin, 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. İçöz, G. “A Kantrovich variant of a new type Bernstein Stancu polynomials”. Appl. Math. Comput. 218, 8552-8560 (2012)
11. Wang, M.L., Yuo, D.S. and Zhou, P. “On the approximation by operators of Bernstein-Stancu types”. Appl. Math. Comput. 246, 79-87 (2014)