Geodesic
Summability Methods in Weighted Approximation to Derivatives of Functions
Serdica Mathematical Journal, Tome 41 (2015) no. 4, pp. 355-368

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In this paper, we use summability methods on the approximation to derivatives of functions by a family of linear operators acting on weighted spaces. This point of view enables us to overcome the lack of ordinary convergence in the approximation. To support this idea, at the end of the paper, we will give a sequence of positive linear operators obeying the arithmetic mean approximation (or, approximation with respect to the Cesàro method) although it is impossible in the usual sense. Some graphical illustrations are also provided. 2010 Mathematics Subject Classification: 41A30, 42B08, 47B38.
Keywords: Summability process, weighted approximation, almost convergence, Cesàro method 
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Küçük, Nisa; Duman, Oktay. Summability Methods in Weighted Approximation to Derivatives of Functions. Serdica Mathematical Journal, Tome 41 (2015) no. 4, pp. 355-368. http://geodesic.mathdoc.fr/item/SMJ2_2015_41_4_a3/