Research Article
BibTex RIS Cite

KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES

Year 2018, Volume: 22 Issue: 6, 1743 - 1751, 01.12.2018

Sevda Yıldız

https://doi.org/10.16984/saufenbilder.383770
Cited By: 3

Abstract

In the present paper, we obtain an abstract version of the Korovkin type theorem via the concept of statistical e-convergence in modular spaces for double sequences of positive linear operators. We give an application showing that the new result is stronger than classical ones. Also, we study an extension to non-positive operators.

Keywords

Statistical e-modular convergence double sequence abstract Korovkin theorem

References

  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Triangular A-statistical approximation by double sequences of positive linear operators. Results Math. 2015; 68: 271-291.
  • Bardaro C., Boccuto A., Demirci K., Mantellini I., Orhan S. Korovkin-type theorems for modular -A-statistical convergence, J. Funct. Spaces. Article ID 160401 2015; 2015:1-11.
  • Bardaro C., Boccuto A., Dimitriou X. and Mantellini I., Abstract Korovkin type theorems in modular spaces and applications, Cent. Eur. J. Math. 2013; 11(10): 1774-1784.
  • Bardaro, C. and Mantellini, I., Korovkin's theorem in modular spaces, Commentationes Math. 2007; 47: 239-253.
  • Bardaro, C., Musielak,J., Vinti,G., Nonlinear integral operators and applications, de Gruyter Series in Nonlinear Analysis and Appl. Vol., 9 Walter de Gruyter Publ., Berlin, 2003.
  • Boccuto, A. and Dimitriou, X., Korovkin-type theorems for abstract modular convergence, Results in Mathematics 2016; 69: 477-495.
  • Boos, J., Leiger, T., Zeller, K. Consistency theory for SM-methods. Acta. Math. Hungar. 1997; 76: 83-116.
  • Boos, J. Classical and modern methods in summability. Oxford University Press Inc., New York, 2000.
  • Demirci K., Orhan S., Statistical relative approximation on modular spaces. Results in Mathematics 2017; 71: 1167-1184.
  • Demirci, K., Kolay, B., A-Statistical Relative Modular Convergence of Positive Linear Operators, Positivity 2017; 21: 847-863.
  • Karaku¸s, S., Demirci, K., Duman, O., Statistical approximation by positive linear operators on modular spaces. Positivity 2010; 14: 321-334.
  • Kozlowski W. M., Modular function spaces, Pure Appl. Math., Vol. 122, Marcel Dekker, Inc., New York, 1988.
  • Kuratowski K., Topology, Volls I and II, Academic Press, New York-London, 1966/1968.
  • Mantellini I., Generalized sampling operators in modular spaces, Commentationes Math. 1998; 38: 77-92.
  • Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Vol. 1034 Springer-Verlag, Berlin, 1983.
  • Musielak J., Nonlinear approximation in some modular function spaces I, Math. Japon. 1993; 38: 83-90.
  • Pringsheim, A. Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 1900; 53: 289-321.
  • Sever, Y., Talo, Ö. Statistical e-convergence of double sequences and its application to Korovkin type approximation theorem for functions of two variables. Iranian Journal of Science and Technology, Transactions A: Science. 2017; 41(3): 851-857.
  • Yilmaz, B., Demirci, K., Orhan, S., Relative Modular Convergence of Positive Linear Operators, Positivity 2016; 20: 565-577.

Year 2018, Volume: 22 Issue: 6, 1743 - 1751, 01.12.2018

Sevda Yıldız

https://doi.org/10.16984/saufenbilder.383770
Cited By: 3

Abstract

References

  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Triangular A-statistical approximation by double sequences of positive linear operators. Results Math. 2015; 68: 271-291.
  • Bardaro C., Boccuto A., Demirci K., Mantellini I., Orhan S. Korovkin-type theorems for modular -A-statistical convergence, J. Funct. Spaces. Article ID 160401 2015; 2015:1-11.
  • Bardaro C., Boccuto A., Dimitriou X. and Mantellini I., Abstract Korovkin type theorems in modular spaces and applications, Cent. Eur. J. Math. 2013; 11(10): 1774-1784.
  • Bardaro, C. and Mantellini, I., Korovkin's theorem in modular spaces, Commentationes Math. 2007; 47: 239-253.
  • Bardaro, C., Musielak,J., Vinti,G., Nonlinear integral operators and applications, de Gruyter Series in Nonlinear Analysis and Appl. Vol., 9 Walter de Gruyter Publ., Berlin, 2003.
  • Boccuto, A. and Dimitriou, X., Korovkin-type theorems for abstract modular convergence, Results in Mathematics 2016; 69: 477-495.
  • Boos, J., Leiger, T., Zeller, K. Consistency theory for SM-methods. Acta. Math. Hungar. 1997; 76: 83-116.
  • Boos, J. Classical and modern methods in summability. Oxford University Press Inc., New York, 2000.
  • Demirci K., Orhan S., Statistical relative approximation on modular spaces. Results in Mathematics 2017; 71: 1167-1184.
  • Demirci, K., Kolay, B., A-Statistical Relative Modular Convergence of Positive Linear Operators, Positivity 2017; 21: 847-863.
  • Karaku¸s, S., Demirci, K., Duman, O., Statistical approximation by positive linear operators on modular spaces. Positivity 2010; 14: 321-334.
  • Kozlowski W. M., Modular function spaces, Pure Appl. Math., Vol. 122, Marcel Dekker, Inc., New York, 1988.
  • Kuratowski K., Topology, Volls I and II, Academic Press, New York-London, 1966/1968.
  • Mantellini I., Generalized sampling operators in modular spaces, Commentationes Math. 1998; 38: 77-92.
  • Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Vol. 1034 Springer-Verlag, Berlin, 1983.
  • Musielak J., Nonlinear approximation in some modular function spaces I, Math. Japon. 1993; 38: 83-90.
  • Pringsheim, A. Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 1900; 53: 289-321.
  • Sever, Y., Talo, Ö. Statistical e-convergence of double sequences and its application to Korovkin type approximation theorem for functions of two variables. Iranian Journal of Science and Technology, Transactions A: Science. 2017; 41(3): 851-857.
  • Yilmaz, B., Demirci, K., Orhan, S., Relative Modular Convergence of Positive Linear Operators, Positivity 2016; 20: 565-577.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sevda Yıldız 0000-0002-4730-2271

Publication Date December 1, 2018
Submission Date January 25, 2018
Acceptance Date May 22, 2018
Published in Issue Year 2018 Volume: 22 Issue: 6

Cite

APA Yıldız, S. (2018). KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES. Sakarya University Journal of Science, 22(6), 1743-1751. https://doi.org/10.16984/saufenbilder.383770
AMA Yıldız S. KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES. SAUJS. December 2018;22(6):1743-1751. doi:10.16984/saufenbilder.383770
Chicago Yıldız, Sevda. “KOROVKIN THEOREM VIA STATISTICAL E-MODULAR CONVERGENCE OF DOUBLE SEQUENCES”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1743-51. https://doi.org/10.16984/saufenbilder.383770.
EndNote Yıldız S (December 1, 2018) KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES. Sakarya University Journal of Science 22 6 1743–1751.
IEEE S. Yıldız, “KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES”, SAUJS, vol. 22, no. 6, pp. 1743–1751, 2018, doi: 10.16984/saufenbilder.383770.
ISNAD Yıldız, Sevda. “KOROVKIN THEOREM VIA STATISTICAL E-MODULAR CONVERGENCE OF DOUBLE SEQUENCES”. Sakarya University Journal of Science 22/6 (December 2018), 1743-1751. https://doi.org/10.16984/saufenbilder.383770.
JAMA Yıldız S. KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES. SAUJS. 2018;22:1743–1751.
MLA Yıldız, Sevda. “KOROVKIN THEOREM VIA STATISTICAL E-MODULAR CONVERGENCE OF DOUBLE SEQUENCES”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1743-51, doi:10.16984/saufenbilder.383770.
Vancouver Yıldız S. KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES. SAUJS. 2018;22(6):1743-51.

Cited By

The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems
Georgian Mathematical Journal
Fadime Dirik
https://doi.org/10.1515/gmj-2020-2075
Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
Mathematica Slovaca
Sevda Yildiz
https://doi.org/10.1515/ms-2021-0046
On new Bézier bases with Schurer polynomials and corresponding results in approximation theory
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Faruk Özger
https://doi.org/10.31801/cfsuasmas.510382
 Download Cover Image

30930  This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.