Approximation by Szasz-Stancu-Durrmeyer type operators using Charlier polynomials

Abdul Wa, Nadeem Rao

Abstract


In the present article, we introduce Szasz-Stancu-Durremeyer type operators using
Charlier polynomials. We discuss uniform convergence in compact interval in terms of Korovkin type theorem and order of approximation using simple modulus of continuity. Moreover, we study order of approximation in some functional spaces with the help of Peetre's K-functional, second order modulus of smoothness and Lipschitz class for these sequences of positive linear operators.


Keywords


Szasz operators, positive linear operators, modulus of continuity, Peetre's K-functional

References


O. Szasz, Generalization of S. Bernstein's polynomials to the innite interval, J. Research

Nat. Bur. Standards, 45, (1950), 239-245.

V. Gupta, R.P. Agarwal, Convergence Estimates in Approximtion Theory, Springer,

Cham., 2014.

M. Mursaleen, Khursheed J. Ansari, On Chlodowsky variant of Szasz operators by

Brenke type polynomials, Appl. Math. Comput, 271, (2015), 991-1003.

A. Wa and N. Rao, Szasz-Durrmeyer operators based on Dunkl analogue, Complex

Anal. Oper. Theory, (2017), DOI 10.1007/s11785-017-0647-7.

T. Acar, (p; q)-Generalization of Szasz-Mirakyan Operators, Mathematical Methods

in the Applied Sciences, (2016), DOI: 10.1002/mma.3721.

A. Wa and N. Rao, A generalization of Szsz-type operators which preserves constant

and quadratic test functions, Cogent Mathematics, (2016), 3:1227023.

A. Wa, N. Rao and Deepmala, Kantorovich form of generalized Szasz-type operators

using Charlier polynomials, Korean Journal of Mathematics, 25 (1), (2017), 99-116.

M. Mursaleen, T. Khan, On approximation by Stancu type Jakimovski-Leviatan-

Durrmeyer operators, Azerbaijan Journal of Mathematics, 7 (1), (2017), 16-26.

S.M. Mazhar, V. Totik, Approximation by modied Szasz operators, Acta Sci. Math.

(Szeged), 49(1-4), (1985), 257-269.

S. Varma, F. Tasdelen, Szasz type operators involving Charlier polynomials, Math.

Comput. Modeling, 56(5-6), (2012), 118-122.

M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in one Variable, Cambridge

University Press, Cambridge, 2005.

A. Kajla, P.N. Agrawal, Szasz-Durrmeyer type operators based on Charlier polynomi-

als, Appl. Math. Comput., 268, (2015), 1001-1014.

N. Rao, A. Wa, Stancu-Variant of Generalized Baskakov Operators, Filomat, 31

(9), (2017), 26432656.

A. Wa, N. Rao and Deepmala, Approximation Properties by Generalized Baskakov

Kantorovich Stancu type operators, Appl. Math. Inf. Sci. Lett. 4 (3), (2016), 1-8.

F. Altomare, M. Campiti, Korovkin-Type approximation Theory and its applications,

of De Gruyter Studies in Mathematics, Appendix A By Michael Pannenberg and Appendix B By Fendinand Beckho, Walter De Gruyter, Berlin, Germany. 17, (1994).

O. Shisha, B. Bond, The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. USA, 60, (1968), 1196-1200.

R.A. DeVore, G.G. Lorentz, Constructive Approximation, Grudlehren der Math-ematischen Wissenschaften [Fundamental principales of Mathematical Sciences], (Springer-Verlag, Berlin, 1993).


Refbacks

  • There are currently no refbacks.


free counters