On Szász-Mirakyan type operators preserving polynomials
DOI:
https://doi.org/10.33993/jnaat461-1087Keywords:
Szász-Mirakyan operators, shape preserving properties, Voronovskaya-type theorem., modified operatorAbstract
In this paper, a modification of Szász-Mirakyan operators is studied [1] which generalizes the Szász-Mirakyan operators with the property that the linear combination
Downloads
References
O. Agratini and S. Tarabie, On approximating operators preserving certain polynomials, Automat. Comput. Appl. Math., 17 (2008), pp. 191-199.
A. Aral, D. Inoan and I. Rasa, On the generalized Szasz-Mirakyan operators, Results in Math., 65 (2014), pp. 441-452, https://doi.org/10.1007/s00025-013-0356-0 DOI: https://doi.org/10.1007/s00025-013-0356-0
P. I. Braica, L I. Piscoran and A. Indrea, Graphical lectures of some King type operators, Acta Univ. Apulensis Math. Inform., 34 (2013), pp. 163-171.
D. Cardenas-Morales, P. Garrancho and F.J. Munoz-Delgado, Shape preserving approximation by Bernstein-type operators which fix polynomials, Appl. Math. Comput., 182 (2006), pp. 1615-1622, https://doi.org/10.1016/j.amc.2006.05.046 DOI: https://doi.org/10.1016/j.amc.2006.05.046
D. Cardenas-Morales, P. Garrancho and I. Rasa, Approximation properties of Bernstein-Durrmeyer type operators, Appl. Math. Comput., 232 (2014), pp. 1-8, http://dx.doi.org/10.1016/j.amc.2014.01.046 DOI: https://doi.org/10.1016/j.amc.2014.01.046
J. de la cal and J. Carcamo, On uniform approximation by some classical Bernstein-type operators, J. Math. Anal. Appl, 279 (2003), pp. 625-638, https://doi.org/10.1016/S0022-247X(03)00048-9 DOI: https://doi.org/10.1016/S0022-247X(03)00048-9
O. Duman and M. Ali Ozarslan, Sz ́asz-Mirakyan type operators providing a better error estimation, Appl. Math. Lett., 20 (2007), pp. 1184-1188, http://dx.doi.org/10.1016/j.aml.2006.10.007 DOI: https://doi.org/10.1016/j.aml.2006.10.007
N. Ispir, On modified Baskakov operators on weighted spaces, Turkish J. Math, 25 (2001), pp. 355-365.
J.P. King, Positive linear operators which preserve x2, Acta Math. Hungar, 99 (2003), pp. 203-208, https://doi.org/10.1023/a:1024571126455 DOI: https://doi.org/10.1023/A:1024571126455
O. Duman and M. Ali Ozarslan, Local approximation properties for certain King type operators, Filomat, 27 (2013), pp. 173-181, https://doi.org/10.2298/FIL1301173O DOI: https://doi.org/10.2298/FIL1301173O
G. M. Phillips, Interpolation and Approximation by Polynomials, Springer-Verlag, New York, 2003, https://doi.org/10.1007/b97417 DOI: https://doi.org/10.1007/b97417
D. D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roumanine Math. Pures Appl., 13 (1968), pp. 1173-1194.
K. G. Weierstrass, Uber Die Analytische Darstel lbarkeit Sogenannter Wil lkurlicher Funktionen Einer Reel len Veranderlichen, Sitzungsber. Akad. Berlin, pp. 633-639, 789-805, 1885.
Z. Ziegler, Linear approximation and generalized convexity , J. Approx. Theory, 1 (1968), pp. 420-443, https://doi.org/10.1016/0021-9045(68)90031-2 DOI: https://doi.org/10.1016/0021-9045(68)90031-2
Published
Issue
Section
License
Copyright (c) 2017 Journal of Numerical Analysis and Approximation Theory

This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.