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Year 2023, Volume: 15 Issue: 1, 180 - 183, 30.06.2023
https://doi.org/10.47000/tjmcs.1221861

Abstract

References

  • Altomare, F., Campiti, M., Korovkin Type Approximation Theory and Its Applications, De Gruyter Studies in Math., vol.17, de Gruyter&Co, Berlin, 1994.
  • Atlıhan, Ö.G., Orhan, C., Summation process of positive linear operators, Computers and Mathematics with Appl., 56(2008), 1188–1195.
  • Atlıhan, Ö.G., Ünver, M., Duman, O., Korovkin theorems on weighted spaces: revisited, Period. Math. Hungar., 75(2017), 201–209.
  • Bardaro, C., Boccuto, A., Dimitriou, X., Mantellini, I., Abstract Korovkin-type theorems in modular spaces and applications, Cent. Eur. J. Math., 11(2013), 1774–1784.
  • Connor, J.S., Two valued measures and summability, Analysis, 10(1990), 373–385.
  • Connor, J.S., R-type summability methods, Cauchy criteria, P-sets and statistical convergence, Proc. Amer. Math. Soc., 115(1992), 319–327.
  • Duman, O., Khan, M.K., Orhan, C., A-statistical convergence of approximating operators, Math. Inequal. Appl., 6(2003), 689–699.
  • Duman, O., Orhan, C., Statistical approximation by positive linear operators, Studia Math., 161(2004), 187–197.
  • Duman, O., Orhan, C., Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett., 18(2005), 1339–1344.
  • Duman, O. Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), 33–46.
  • Fast, H., Sur la convergence statistique, In Colloquium mathematicae, 2(1951), 241–244.
  • Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–314.
  • Fridy, J.A., Miller, H.I., Orhan, C., Statistical rates of convergence, Acta Sci. Math., 69(2003), 147–157.
  • Gadziev, A.D., The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P. P. Korovkin, Soviet Math. Dokl., 15(1974), 1433–1436.
  • Gadjiev, A.D., On P.P. Korovkin type theorems, Mat. Zametki, 20(1976), 781–786.
  • Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain Journal of Math., 32(2002), 129–137.
  • Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Doklady Akad. Nauk SSR., 90(1953), 961–964.
  • Miller, H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(1995), 1811–1819.
  • Popa, D., An operator version of the Korovkin theorem, J. Math. Anal. Appl., 515(2022), Article No: 126375.
  • Salat, T., On statistically convergent sequences of real numbers, Mat. Slovaca., 30(1980), 139–150.
  • Unver, M., Orhan, C., Statistical convergence with respect to power series methods and applications to approximation theory, Numerical Functional Analysis and Optimization, 40(2019), 535–547.
  • Micchelli, C.A., Convergence of positive linear operators on C(X), J. Approx. Theory, 13(1975), 305–315.

On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence

Year 2023, Volume: 15 Issue: 1, 180 - 183, 30.06.2023
https://doi.org/10.47000/tjmcs.1221861

Abstract

An operator version of the Korovkin theorem has recently been obtained by D. Popa. With the motivation of this result, we have extended it by using a more powerful convergence which also includes ordinary convergence. We have also presented an example to illustrate the strength of our theorem.

References

  • Altomare, F., Campiti, M., Korovkin Type Approximation Theory and Its Applications, De Gruyter Studies in Math., vol.17, de Gruyter&Co, Berlin, 1994.
  • Atlıhan, Ö.G., Orhan, C., Summation process of positive linear operators, Computers and Mathematics with Appl., 56(2008), 1188–1195.
  • Atlıhan, Ö.G., Ünver, M., Duman, O., Korovkin theorems on weighted spaces: revisited, Period. Math. Hungar., 75(2017), 201–209.
  • Bardaro, C., Boccuto, A., Dimitriou, X., Mantellini, I., Abstract Korovkin-type theorems in modular spaces and applications, Cent. Eur. J. Math., 11(2013), 1774–1784.
  • Connor, J.S., Two valued measures and summability, Analysis, 10(1990), 373–385.
  • Connor, J.S., R-type summability methods, Cauchy criteria, P-sets and statistical convergence, Proc. Amer. Math. Soc., 115(1992), 319–327.
  • Duman, O., Khan, M.K., Orhan, C., A-statistical convergence of approximating operators, Math. Inequal. Appl., 6(2003), 689–699.
  • Duman, O., Orhan, C., Statistical approximation by positive linear operators, Studia Math., 161(2004), 187–197.
  • Duman, O., Orhan, C., Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett., 18(2005), 1339–1344.
  • Duman, O. Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), 33–46.
  • Fast, H., Sur la convergence statistique, In Colloquium mathematicae, 2(1951), 241–244.
  • Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–314.
  • Fridy, J.A., Miller, H.I., Orhan, C., Statistical rates of convergence, Acta Sci. Math., 69(2003), 147–157.
  • Gadziev, A.D., The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P. P. Korovkin, Soviet Math. Dokl., 15(1974), 1433–1436.
  • Gadjiev, A.D., On P.P. Korovkin type theorems, Mat. Zametki, 20(1976), 781–786.
  • Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain Journal of Math., 32(2002), 129–137.
  • Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Doklady Akad. Nauk SSR., 90(1953), 961–964.
  • Miller, H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(1995), 1811–1819.
  • Popa, D., An operator version of the Korovkin theorem, J. Math. Anal. Appl., 515(2022), Article No: 126375.
  • Salat, T., On statistically convergent sequences of real numbers, Mat. Slovaca., 30(1980), 139–150.
  • Unver, M., Orhan, C., Statistical convergence with respect to power series methods and applications to approximation theory, Numerical Functional Analysis and Optimization, 40(2019), 535–547.
  • Micchelli, C.A., Convergence of positive linear operators on C(X), J. Approx. Theory, 13(1975), 305–315.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Tuğba Yurdakadim 0000-0003-2522-6092

Emre Taş 0000-0002-6569-626X

Publication Date June 30, 2023
Published in Issue Year 2023 Volume: 15 Issue: 1

Cite

APA Yurdakadim, T., & Taş, E. (2023). On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. Turkish Journal of Mathematics and Computer Science, 15(1), 180-183. https://doi.org/10.47000/tjmcs.1221861
AMA Yurdakadim T, Taş E. On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. TJMCS. June 2023;15(1):180-183. doi:10.47000/tjmcs.1221861
Chicago Yurdakadim, Tuğba, and Emre Taş. “On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence”. Turkish Journal of Mathematics and Computer Science 15, no. 1 (June 2023): 180-83. https://doi.org/10.47000/tjmcs.1221861.
EndNote Yurdakadim T, Taş E (June 1, 2023) On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. Turkish Journal of Mathematics and Computer Science 15 1 180–183.
IEEE T. Yurdakadim and E. Taş, “On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence”, TJMCS, vol. 15, no. 1, pp. 180–183, 2023, doi: 10.47000/tjmcs.1221861.
ISNAD Yurdakadim, Tuğba - Taş, Emre. “On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence”. Turkish Journal of Mathematics and Computer Science 15/1 (June 2023), 180-183. https://doi.org/10.47000/tjmcs.1221861.
JAMA Yurdakadim T, Taş E. On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. TJMCS. 2023;15:180–183.
MLA Yurdakadim, Tuğba and Emre Taş. “On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 1, 2023, pp. 180-3, doi:10.47000/tjmcs.1221861.
Vancouver Yurdakadim T, Taş E. On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. TJMCS. 2023;15(1):180-3.