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An application of almost convergence in approximation theorems. (English) Zbl 1252.41022
Summary: The concept of almost convergence was introduced by G. G. Lorentz [Acta Math., Uppsala 80, 167–190 (1948; Zbl 0031.29501)] has various applications. In this work, we apply this method to prove some Korovkin-type approximation theorems.
MSC:
41A36Approximation by positive operators
References:
[1]S. Banach, Théorie des Operations Lineaires, Warsaw, 1932. · Zbl 0005.20901
[2]Lorentz, G. G.: A contribution to theory of divergent sequences, Acta math. 80, 167-190 (1948) · Zbl 0031.29501 · doi:10.1007/BF02393648
[3]Gadziev, A. D.: The convergence problems for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P.P. Korovkin, Soviet math. Dokl. 15, 1433-1436 (1974) · Zbl 0312.41013
[4]Dirik, F.; Demirci, K.: Korovkin type approximation theorem for functions of two variables in statistical sense, Turk. J. Math. 33, 1-11 (2009)
[5]Edely, O. H. H.; Mohiuddine, S. A.; Noman, A. K.: Korovkin type approximation theorems obtained through generalized statistical convergence, Appl. math. Lett. 23, No. 11, 1382-1387 (2010) · Zbl 1206.40003 · doi:10.1016/j.aml.2010.07.004
[6]Ahmad, Z. U.; Mursaleen: An application of Banach limits, Proc. amer. Math. soc. 103, No. 1, 244-246 (1988) · Zbl 0652.40009 · doi:10.2307/2047559