On Approximation by Stancu Type Jakimovski-Leviatan- Durrmeyer Operators

M. Mursaleen, T. Khan


In this paper we introduce and study the Stancu type generalization of the Jakimovski-Leviatan-Durrmeyer operators and examine their approximation properties. We investigate the convergence of these operators with the help of Korovkin’s approximation theorem. Also, we study local approximation properties and some direct theorems for these operators.


Szász operators, Favard-Szász operators, Appell polynomials, Jaki- movski-Leviatan-Durrmeyer operators, modulus of continuity, positive linear operators, Korovkin type approximation theorem, local approximation, weighted space.


C. Atakut, I. Büyükyazici, Stancu type generalization of the Favard-Szász operators, Appl. Math. Lett., 23, 2010, 1479-1482.

I. Büyükyazici, H. Tanberkan, S.K. Serenbay, C. Atakut, Approximation by Chlodowsky type Jakimovski-Leviatan operators, J. Comput. Appl. Math., 259, 2014, 153-163.

A. Ciupa, Approximation properties of a modified Jakimovski-Leviatan operator, Automat. Comput. Appl. Math., 17(3), 2008, 401-408.

S.G. Gal, Approximation and geometric properties of complex Favard-Szász-Mirakyan operators in compact disks, Comput. Math. Appl., 56(4), 2008, 1121-1127.

S.S. Guo, G.S. Zhang, L. Liu, Pointwise approximation by Szász-Mirakyan quasiinterpolants, J. Math. Res. Exposition, 29(4), 2009, 629-638.

V. Gupta, A. Aral, M.A. Noor, M.S. Beniwal, Rate of convergence in simultanous approximation for Szász-Mirakyan-Durrmeyer operators, J. Math. Anal. Appl., 322(2), 2006, 964-970.

M.E.H. Ismail, On a generalization of Szász operators, Mathematica (Cluj), 39, 1974, 259-267.

A. Jakimovski, D. Leviatan, Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj), 34, 1969, 97-103.

A. Karaisa, Approximation by Durrmeyer type Jakimovski-Leviatan operators, Math. Methods Appl. Sci., 2015, DOI: 10.1002/mma.3650.

P.P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publishing Corporation, Delhi, 1960.

D. Kumar, G.R. Kumar, J. Shipra, Rate of approximation for certain Szász-Mirakyan-Durrmeyer operators, Georgian Math. J., 16(3), 2009, 475-487.

R.N. Mehrotra, Z. Walczak, Remarks on a class of Szász-Mirakyan type operators, East J. Approx., 15(2), 2009, 197-206.

M. Mursaleen, Applied Summability Methods, Springer Briefs, Heidelberg-New York-Dordrecht-London, 2014.

M. Mursaleen, K.J. Ansari, On Chlodowsky variant of Szász operators by Brenke type polynomials, Appl. Math. Comput., 271, 2015, 991-1003.

D. Stancu, A study of the remainder in an approximation formula using a Favard-Szász type operator, Stud. Univ. Babe¸ s-Bolyai Math., XXV, 1980, 70-76.

O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Natl. Bur. Stand., 45, 1950, 239-245.

R.A. De Vore, G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.


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