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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 514174, 7 pages
http://dx.doi.org/10.1155/2013/514174
Research Article

A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators

Department of Mathematics, Faculty of Arts and Sciences, Bulent Ecevit University, 67100 Zonguldak, Turkey

Received 25 January 2013; Revised 17 April 2013; Accepted 18 April 2013

Academic Editor: Adem Kılıçman

Copyright © 2013 Yusuf Kaya and Nazmiye Gönül. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Altomore and M. Campiti, Korovkin Type Approximation Theory and Its Application, Walter de Gruyter, Berlin, Germany, 1994.
  2. R. A. DeVore, The Approximation of Continuous Functions by Positive Linear Operators, vol. 293 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1972. View at MathSciNet
  3. P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan, New Delhi, India, 1960. View at MathSciNet
  4. M. Mursaleen and A. Kiliçman, “Korovkin second theorem via B-statistical A-summability,” Abstract and Applied Analysis, vol. 2013, Article ID 598963, 6 pages, 2013. View at Publisher · View at Google Scholar
  5. H. M. Srivastava, M. Mursaleen, and A. Khan, “Generalized equi-statistical convergence of positive linear operators and associated approximation theorems,” Mathematical and Computer Modelling, vol. 55, no. 9-10, pp. 2040–2051, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Balcerzak, K. Dems, and A. Komisarski, “Statistical convergence and ideal convergence for sequences of functions,” Journal of Mathematical Analysis and Applications, vol. 328, no. 1, pp. 715–729, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. Erkuş and O. Duman, “A Korovkin type approximation theorem in statistical sense,” Studia Scientiarum Mathematicarum Hungarica, vol. 43, no. 3, pp. 285–294, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Aktuğlu and H. Gezer, “Lacunary equi-statistical convergence of positive linear operators,” Central European Journal of Mathematics, vol. 7, no. 3, pp. 558–567, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Ö. Çakar and A. D. Gadjiev, “On uniform approximation by Bleimann, Butzer and Hahn operators on all positive semiaxis,” Transactions of Academy of Sciences of Azerbaijan, Series of Physical-Technical and Mathematical Sciences, vol. 19, no. 5, pp. 21–26, 1999. View at Zentralblatt MATH · View at MathSciNet
  10. S. Karakuş, K. Demirci, and O. Duman, “Equi-statistical convergence of positive linear operators,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1065–1072, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. O. Duman, M. K. Khan, and C. Orhan, “A-statistical convergence of approximating operators,” Mathematical Inequalities and Applications, vol. 6, no. 4, pp. 689–699, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet