SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES

Yıl 2016, Cilt: 65 Sayı: 2, 65 - 76, 01.08.2016

T. Yurdakadım

https://doi.org/10.1501/Commua1_0000000760

Cited By: 8

Öz

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.

Anahtar Kelimeler

Power series method, modular spaces, abstract Korovkin theory

Kaynakça

• 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 : [e-mail]