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 Volume 4, Issue 11 (November 2017), Pages: 78-80


 Original Research Paper

 Title: Lacunary statistical convergence of Bernstein operator sequences

 Author(s): Ayhan Esi 1, Serkan Araci 2, *


 1Department of Mathematics, Science and Arts Faculty, Adiyaman University, TR-02040, Adiyaman, Turkey
 2Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey

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The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. Recently the statistical convergence of Bernstein operators was studied. In this paper, by using the concept of natural density and lacunary sequences we first introduce the notion of lacunary statistical convergence of a sequence of Bernstein polynomials. Next we apply this notion to VBΘ-summability. We also investigate some inclusion relations related to these concepts. 

 © 2017 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (

 Keywords: Statistical convergence lacunary sequence, Strongly Cesaro summable, Bernstein operators

 Article History: Received 1 November 2016, Received in revised form 2 August 2017, Accepted 2 September 2017

 Digital Object Identifier:


 Esi A and  Araci S (2017). Lacunary statistical convergence of Bernstein operator sequences. International Journal of Advanced and Applied Sciences, 4(11): 78-80

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