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SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES

Year 2016, Volume: 65 Issue: 2, 65 - 76, 01.08.2016
https://doi.org/10.1501/Commua1_0000000760

Abstract

In this paper, we obtain a Korovkin type approximation result
for a sequence of positive linear operators defined on modular spaces with the
use of power series method . We also provide an example which satisfies our
theorem.

References

  • F. Altomare and S. Diomede, Contractive Korovkin subsets in weighted spaces of continuous functions. Rend. Circ. Mat. Palermo 50 (2001), 547-568.
  • F. Altomare, Korovkin-type theorems and approximation by positive linear operators. Sur- veys in Approximation Theory 5.13 (2010).
  • C. Bardaro, I. Mantellini, Approximation properties in abstract modular spaces for a class of general sampling-type operators. Appl. Anal. 85 (2006), 383-413.
  • C. Bardaro, I. Mantellini, Korovkin’s theorem in modular spaces. Comment. Math. 47 (2007), 253.
  • C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, Modular …lter convergence theorems for abstract sampling-type operators. Appl. Anal. 92 (2013), 2404-2423.
  • C. Bardaro, I. Mantellini, Multivariate moment type operators: approximation properties in Orlicz spaces. J. Math. Ineq. 2 (2008), 247-259.
  • C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, A Korovkin theorem in multivariate modular function spaces. J. Func. Spaces Appl., 7 (2009), 105-120.
  • C. Bardaro, J. Musielak, G. Vinti, Nonlinear Integral Operators and Applications. De Gruyter Ser. Nonlinear Anal. Appl. 9, Walter de Gruyter, Berlin (2003).
  • C. Bardaro, A. Boccuto, X. Dimitriou and I. Mantellini, Abstract korovkin type theorems in modular spaces and applications. Cent. Eur. J. Math., 11 (2013), 1774-1784.
  • C. Belen, M. Yildirim, Statistical approximation in multivariate modular function spaces. Comment. Math. 51 (2011), 39-53.
  • A. Boccuto, X. Dimitriou, Modular …lter convergence theorems for Urysohn integral operators and applications. Acta Math. Sinica, 29 (2013), 1055-1066.
  • J. Boos, Classical and Modern Methods in Summability. Oxford University Press (2000).
  • P. L. Butzer and H. Berens, Semi-groups of operators and approximation. Die Grundlehren der Mathematischen Wissenschaften, 145, Springer, New York, (1967).
  • A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32 (2002), 129-138.
  • S. Karakus, K. Demirci, O. Duman, Statistical approximation by positive linear operators on modular spaces. Positivity, 14 (2010), 321-334.
  • S. Karakus, K. Demirci, Matrix summability and Korovkin type approximation theorem on modular spaces. Acta Math. Univ. Commenianae, 2 (2010), 281-292.
  • P. P. Korovkin, Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi, (1960).
  • W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability. J. Math. Anal. Appl. (1989), 362-371.
  • J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer, Berlin (1983).
  • J. Musielak and W. Orlicz, On modular spaces. Studia Math. 18 (1959), 49-65.
  • U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods. J. Math. Anal. Appl. 238 (1999), 44-66.
  • E. Tas, Some results concerning Mastroianni operators by power series method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 63(1) (2016), 187-195.
  • Current address : Department of Mathematics, Hitit University, Çorum, Turkey E-mail address : tugbayurdakadim@hotmail.com
Year 2016, Volume: 65 Issue: 2, 65 - 76, 01.08.2016
https://doi.org/10.1501/Commua1_0000000760

Abstract

References

  • F. Altomare and S. Diomede, Contractive Korovkin subsets in weighted spaces of continuous functions. Rend. Circ. Mat. Palermo 50 (2001), 547-568.
  • F. Altomare, Korovkin-type theorems and approximation by positive linear operators. Sur- veys in Approximation Theory 5.13 (2010).
  • C. Bardaro, I. Mantellini, Approximation properties in abstract modular spaces for a class of general sampling-type operators. Appl. Anal. 85 (2006), 383-413.
  • C. Bardaro, I. Mantellini, Korovkin’s theorem in modular spaces. Comment. Math. 47 (2007), 253.
  • C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, Modular …lter convergence theorems for abstract sampling-type operators. Appl. Anal. 92 (2013), 2404-2423.
  • C. Bardaro, I. Mantellini, Multivariate moment type operators: approximation properties in Orlicz spaces. J. Math. Ineq. 2 (2008), 247-259.
  • C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, A Korovkin theorem in multivariate modular function spaces. J. Func. Spaces Appl., 7 (2009), 105-120.
  • C. Bardaro, J. Musielak, G. Vinti, Nonlinear Integral Operators and Applications. De Gruyter Ser. Nonlinear Anal. Appl. 9, Walter de Gruyter, Berlin (2003).
  • C. Bardaro, A. Boccuto, X. Dimitriou and I. Mantellini, Abstract korovkin type theorems in modular spaces and applications. Cent. Eur. J. Math., 11 (2013), 1774-1784.
  • C. Belen, M. Yildirim, Statistical approximation in multivariate modular function spaces. Comment. Math. 51 (2011), 39-53.
  • A. Boccuto, X. Dimitriou, Modular …lter convergence theorems for Urysohn integral operators and applications. Acta Math. Sinica, 29 (2013), 1055-1066.
  • J. Boos, Classical and Modern Methods in Summability. Oxford University Press (2000).
  • P. L. Butzer and H. Berens, Semi-groups of operators and approximation. Die Grundlehren der Mathematischen Wissenschaften, 145, Springer, New York, (1967).
  • A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32 (2002), 129-138.
  • S. Karakus, K. Demirci, O. Duman, Statistical approximation by positive linear operators on modular spaces. Positivity, 14 (2010), 321-334.
  • S. Karakus, K. Demirci, Matrix summability and Korovkin type approximation theorem on modular spaces. Acta Math. Univ. Commenianae, 2 (2010), 281-292.
  • P. P. Korovkin, Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi, (1960).
  • W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability. J. Math. Anal. Appl. (1989), 362-371.
  • J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer, Berlin (1983).
  • J. Musielak and W. Orlicz, On modular spaces. Studia Math. 18 (1959), 49-65.
  • U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods. J. Math. Anal. Appl. 238 (1999), 44-66.
  • E. Tas, Some results concerning Mastroianni operators by power series method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 63(1) (2016), 187-195.
  • Current address : Department of Mathematics, Hitit University, Çorum, Turkey E-mail address : tugbayurdakadim@hotmail.com
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

T. Yurdakadım This is me

Publication Date August 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 2

Cite

APA Yurdakadım, T. (2016). SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 65-76. https://doi.org/10.1501/Commua1_0000000760
AMA Yurdakadım T. SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2016;65(2):65-76. doi:10.1501/Commua1_0000000760
Chicago Yurdakadım, T. “SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 2 (August 2016): 65-76. https://doi.org/10.1501/Commua1_0000000760.
EndNote Yurdakadım T (August 1, 2016) SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 65–76.
IEEE T. Yurdakadım, “SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 2, pp. 65–76, 2016, doi: 10.1501/Commua1_0000000760.
ISNAD Yurdakadım, T. “SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (August 2016), 65-76. https://doi.org/10.1501/Commua1_0000000760.
JAMA Yurdakadım T. SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:65–76.
MLA Yurdakadım, T. “SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 2, 2016, pp. 65-76, doi:10.1501/Commua1_0000000760.
Vancouver Yurdakadım T. SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):65-76.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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