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Statistically Relatively A−summability of Convergence of Double Sequences of Positive Linear Operators

Year 2017, Volume: 2 Issue: 1, 59 - 66, 01.07.2017

Abstract

In this paper, we introduce the concept of statistically relatively A-summability. Based upon this definition and A-statistically relatively uniform convergence for double sequences of functions, we prove a Korovkin-type approximation theorem and give a strong example. Also, we study the rates of statistical relatively A−summability of positive linear operators.

References

  • F. Altomare and M. Campiti, Korovkin Type Approximation Theory and Its Application, Walter de Gruyter Publ., Berlin (1994)
  • 2. Anastassiou, G. A. and Duman, O., A Baskakov type generalization of statistical Korovkin theory. J. Math. Anal. Appl. 340, 476-486 (2008)
  • 3. Anastassiou, G. A. and Duman, O., Statistical fuzzy approximation by fuzzy positive linear operators. Compt. Math. Appl. 55, 573-580, (2008)
  • 4. E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15, 197-201 (1914)
  • 5. E. W. Chittenden, On the limit functions of sequences of continuous functions converging relatively uniformly, Transactions of the AMS, 20, 179-184 (1919)
  • 6. E. W. Chittenden, Relatively uniform convergence and classi cation of functions, Transactions of the AMS, 23, 1-15, (1922)
  • 7. F. Dirik and K. Demirci, Korovkin Type Approximation Theorem for Functions of Two Variables in Statistical Sense, Turk J. Math. 34, 73-83, (2010)
  • 8. Hamilton, H. J., Transformations of multiple sequences, Duke Math. J. 2, 29-60 (1936)
  • 9. G. H. Hardy, Divergent series, Oxford Uni. Press, London, (1949)
Year 2017, Volume: 2 Issue: 1, 59 - 66, 01.07.2017

Abstract

References

  • F. Altomare and M. Campiti, Korovkin Type Approximation Theory and Its Application, Walter de Gruyter Publ., Berlin (1994)
  • 2. Anastassiou, G. A. and Duman, O., A Baskakov type generalization of statistical Korovkin theory. J. Math. Anal. Appl. 340, 476-486 (2008)
  • 3. Anastassiou, G. A. and Duman, O., Statistical fuzzy approximation by fuzzy positive linear operators. Compt. Math. Appl. 55, 573-580, (2008)
  • 4. E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15, 197-201 (1914)
  • 5. E. W. Chittenden, On the limit functions of sequences of continuous functions converging relatively uniformly, Transactions of the AMS, 20, 179-184 (1919)
  • 6. E. W. Chittenden, Relatively uniform convergence and classi cation of functions, Transactions of the AMS, 23, 1-15, (1922)
  • 7. F. Dirik and K. Demirci, Korovkin Type Approximation Theorem for Functions of Two Variables in Statistical Sense, Turk J. Math. 34, 73-83, (2010)
  • 8. Hamilton, H. J., Transformations of multiple sequences, Duke Math. J. 2, 29-60 (1936)
  • 9. G. H. Hardy, Divergent series, Oxford Uni. Press, London, (1949)
There are 9 citations in total.

Details

Journal Section Research Articles
Authors

Fadime Dirik

Pınar Okçu Şahin This is me

Publication Date July 1, 2017
Submission Date October 24, 2016
Published in Issue Year 2017 Volume: 2 Issue: 1

Cite

APA Dirik, F., & Okçu Şahin, P. (2017). Statistically Relatively A−summability of Convergence of Double Sequences of Positive Linear Operators. Sinop Üniversitesi Fen Bilimleri Dergisi, 2(1), 59-66.


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