International Journal of Nonlinear Analysis and Applications

On approximation by Szasz-Mirakyan-Schurer-Kantrovich operators preserving $e^{−bx}, b > 0$

Document Type : Research Paper

Authors

1 aUniversity of Anbar, Education College for women, Ramadi, Iraq

2 University of Anbar, Education College for pure science, Department of Mathematics, Ramadi, Iraq

Abstract

Through this treatise, a study has been submitted about modified of Szasz-Mirakyan-Schurer-Kantrovich operators which that preserving \(e^{- bx\ },b > 0\) function. We interpret and study the uniform convergence of the modern operators to \(\text{\ f}\). Also, by analyzing the asymptotic conduct of our operator.

Keywords

[1] T. Acar, A. Aral and H. Gonska, On Szasz–Mirakyan operators preserving e
2ax, a > 0, Mediterr. J. Math. 14
(2017) 1–14.
[2] J. M. Aldaz and H. Render, Optimality of generalized Bernstein operators, J. Approx. Theory 162 (2010) 1407–
1416.
[3] F. Altomare, M. Cappelletti and V. Leonessa, On a generalization of Sz´asz–Mirakjan–Kantorovich operators,
Results Math. 63 (2012) 837–863.
[4] K. J. Ansari, M. Mursaleen, K.P.M. Shareef and M. Ghouse, Approximation by modified Kantorovich-Sz´asz type
operators involving Charlier polynomials, Adv. Diff. Equ. 1 (2020).
[5] A. Aral, D. Inoan and I. Ra¸sa, Approximation properties of Sz´asz–Mirakyan operators preserving exponential
functions, Positivity, 23 (2019) 233–246.
[6] R. Aslan and A. ˙Izgi,Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and
Associated GBS Operators on Symmetrical Mobile Interval, J. Funct. Spaces 2021, Article ID 9979286, 12 pages.
[7] M. Bodur, H. Karsli and F. Ta¸sdelen, Urysohn Type Schurer Operators, Results Math. 75 (2020) 96.
[8] E. Deniz, A. Aral and V. Gupta, Note on Sz´asz-Mirakyan-Durrmeyer operators preserving e
2ax, a > 0, Numerical
Funct. Anal. Opt. 39 (2018) 201–207.
[9] O. Duman, M.A. Ozarslan and B. Della Vecchia,Modified Sz´asz–Mirakjan–Kantorovich operators preserving linear
functions, Turk. J. Math. 33 (2009) 151–158.
[10] S. A. Holho, The rate of approximation of functions in an infinite interval by positive linear operators, Stud.
Univ. Babe¸s-Bolyai Math. 2 (2010) 133–142.
[11] L.V. Kantorovich, Sur Certain Developpements Suivant les Polynomes de la Forme de S. Bernstein, I, II, C.R.
Acad. URSS, 1930.
[12] A. Kumar and R. Pratap, Approximation by modified Sz´asz-Kantorovich type operators based on Brenke type
polynomials, Ann. Dell’Univ. Ferrara 22 (2021) 1–8.
[13] F. Schurer,Linear Positive Operators in Approximation Theory, Math. Inst. Techn. Univ. Delft Report, 1962.
[14] O. Sz´asz, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Natl. Bur. Stand. 45 (1950)
239–245.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 2351-2358
  • Receive Date: 05 March 2021
  • Revise Date: 27 June 2021
  • Accept Date: 12 July 2021