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2013 | 11 | 10 | 1774-1784
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Abstract Korovkin-type theorems in modular spaces and applications

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EN
Abstrakty
EN
We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.
Twórcy
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy, bardaro@unipg.it
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy, boccuto@yahoo.it
  • Department of Mathematics, University of Athens, Panepistimiopolis, Athens, 15784, Greece, xenofon11@gmail.com
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy, mantell@dmi.unipg.it
Bibliografia
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  • [3] Altomare F., Korovkin-type theorems and approximation by positive linear operators, Surv. Approx. Theory, 2010, 5, 92–164
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  • [5] Anastassiou G.A., Duman O., Towards Intelligent Modeling: Statistical Approximation Theory, Intell. Syst. Ref. Libr., 14, Springer, Berlin, 2011 http://dx.doi.org/10.1007/978-3-642-19826-7[Crossref]
  • [6] Bardaro C., Boccuto A., Dimitriou X., Mantellini I., Modular filter convergence theorems for abstract sampling-type operators, Appl. Anal. (in press), DOI: 10.1080/00036811.2012.738480 [Crossref]
  • [7] Bardaro C., Mantellini I., Multivariate moment type operators: approximation properties in Orlicz spaces, J. Math. Inequal., 2008, 2(2), 247–259 http://dx.doi.org/10.7153/jmi-02-22[Crossref]
  • [8] Bardaro C., Mantellini I., A Korovkin theorem in multivariate modular function spaces, J. Funct. Spaces Appl., 2009, 7(2), 105–120 http://dx.doi.org/10.1155/2009/863153[Crossref]
  • [9] Bardaro C., Musielak J., Vinti G., Nonlinear Integral Operators and Applications, De Gruyter Ser. Nonlinear Anal. Appl., 9, Walter de Gruyter, Berlin, 2003 http://dx.doi.org/10.1515/9783110199277[Crossref]
  • [10] Belen C., Yildirim M., Statistical approximation in multivariate modular function spaces, Comment. Math., 2011, 51(1), 39–53
  • [11] Boccuto A., Candeloro D., Integral and ideals in Riesz spaces, Inform. Sci., 2009, 179(17), 2891–2902 http://dx.doi.org/10.1016/j.ins.2008.11.001[Crossref]
  • [12] Boccuto A., Dimitriou X., Modular filter convergence theorems for Urysohn integral operators and applications, Acta Math. Sinica, 2013, 29(6), 1055–1066 http://dx.doi.org/10.1007/s10114-013-1443-6[Crossref][WoS]
  • [13] Boccuto A., Dimitriou X., Modular convergence theorems for integral operators in the context of filter exhaustiveness and applications, Mediterr. J. Math., 2013, 10(2), 823–842 http://dx.doi.org/10.1007/s00009-012-0199-z[WoS][Crossref]
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  • [18] Karakuş S., Demirci K., Duman O., Statistical approximation by positive linear operators on modular spaces, Positivity, 2010, 14(2), 321–334 http://dx.doi.org/10.1007/s11117-009-0020-9[Crossref][WoS]
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0288-7
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