Araştırma Makalesi
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KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES

Yıl 2018, Cilt: 22 Sayı: 6, 1743 - 1751, 01.12.2018
https://doi.org/10.16984/saufenbilder.383770

Öz

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.

Kaynakça

  • 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.
Yıl 2018, Cilt: 22 Sayı: 6, 1743 - 1751, 01.12.2018
https://doi.org/10.16984/saufenbilder.383770

Öz

Kaynakça

  • 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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Sevda Yıldız 0000-0002-4730-2271

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 25 Ocak 2018
Kabul Tarihi 22 Mayıs 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 6

Kaynak Göster

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. Aralık 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, sy. 6 (Aralık 2018): 1743-51. https://doi.org/10.16984/saufenbilder.383770.
EndNote Yıldız S (01 Aralık 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, c. 22, sy. 6, ss. 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 (Aralık 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, c. 22, sy. 6, 2018, ss. 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.

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