Abstract
In this chapter, using power series method we study some Korovkin type approximation theorems which deal with the problem of approximating a function by means of a sequence of linear operators acting on weighted spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
O. Agratini, Statistical convergence of a non-positive approximation process. Chaos Solitons Fractals 44, 977–981 (2011)
F. Altomare, Korovkin-type theorems and approximation by positive linear operators. Surv. Approx. Theory 5, 92–164 (2010)
G.A. Anastassiou, O. Duman, Statistical weighted approximation to derivatives of functions by linear operators. J. Comput. Anal. Appl. 11, 20–30 (2009)
Ö.G. Atlihan, E. Taş, An abstract version of the Korovkin theorem via A-summation process. Acta Math. Hung. 145, 360–368 (2015)
J. Boos, Classical and Modern Methods in Summability (Oxford University Press, Oxford, 2000)
K. Demirci, F. Dirik, Statistical \(\sigma\)-convergence of positive linear operators. Appl. Math. Lett. 24, 375–380 (2011)
O. Duman, C. Orhan, An abstract version of the Korovkin approximation theorem. Publ. Math. Debr. 69, 33–46 (2006)
R.O. Efendiev, Conditions for convergence of linear operators to derivatives (Russian). Akad. Nauk. Azerb. SSR Dokl. 40, 3–6 (1984)
W. Kratz, U. Stadtmüller, Tauberian theorems for J p -summability. J. Math. Anal. Appl. 139, 362–371 (1989)
N. Küçük, O. Duman, Summability methods in weighted approximation to derivatives of functions. Serdica Math. J. 41, 335–368 (2015)
T. Nishishiraho, Quantitative equi-uniform approximation processes of integral operators in Banach spaces. Taiwan. J. Math. 10, 441–465 (2006)
I. Özgüç, E. Taş, A Korovkin-type approximation theorem and power series method. Results Math. doi:10.1007/s00025_016_0538_7 (2016)
U. Stadtmüller, A. Tali, On certain families of generalized Nörlund methods and power series methods. J. Math. Anal. Appl. 238, 44–66 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Taş, E., Yurdakadim, T. (2016). Approximation to Derivatives of Functions by Linear Operators Acting on Weighted Spaces by Power Series Method. In: Anastassiou, G., Duman, O. (eds) Computational Analysis. Springer Proceedings in Mathematics & Statistics, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-319-28443-9_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-28443-9_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28441-5
Online ISBN: 978-3-319-28443-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)