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http://dx.doi.org/10.5666/KMJ.2018.58.4.733

Density by Moduli and Korovkin Type Approximation Theorem of Boyanov and Veselinov  

Bhardwaj, Vinod K. (Department of Mathematics, Kurukshetra University)
Dhawan, Shweta (Department of Mathematics, KVA DAV College for Women Karnal-132001)
Publication Information
Kyungpook Mathematical Journal / v.58, no.4, 2018 , pp. 733-746 More about this Journal
Abstract
The concept of f-statistical convergence which is, in fact, a generalization of statistical convergence, has been introduced recently by Aizpuru et al. (Quaest. Math. 37: 525-530, 2014). The main object of this paper is to prove an f-statistical analog of the classical Korovkin type approximation theorem of Boyanov and Veselinov. It is shown that the f-statistical analog is intermediate between the classical theorem and its statistical analog. As an application, we estimate the rate of f-statistical convergence of the sequence of positive linear operators defined from $C^*[0,{\infty})$ into itself.
Keywords
modulus function; statistical convergence; positive linear operator; rate of convergence; Korovkin type approximation theorem;
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