TY - JOUR T1 - SOME KOROVKIN TYPE RESULTS VIA POWER SERIES METHOD IN MODULAR SPACES AU - Yurdakadım, T. PY - 2016 DA - August DO - 10.1501/Commua1_0000000760 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 65 EP - 76 VL - 65 IS - 2 LA - en AB - 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. KW - Power series method KW - modular spaces KW - abstract Korovkin theory CR - F. Altomare and S. Diomede, Contractive Korovkin subsets in weighted spaces of continuous functions. Rend. Circ. Mat. Palermo 50 (2001), 547-568. CR - F. Altomare, Korovkin-type theorems and approximation by positive linear operators. Sur- veys in Approximation Theory 5.13 (2010). CR - C. Bardaro, I. Mantellini, Approximation properties in abstract modular spaces for a class of general sampling-type operators. Appl. Anal. 85 (2006), 383-413. CR - C. Bardaro, I. Mantellini, Korovkin’s theorem in modular spaces. Comment. Math. 47 (2007), 253. CR - C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, Modular …lter convergence theorems for abstract sampling-type operators. Appl. Anal. 92 (2013), 2404-2423. CR - C. Bardaro, I. Mantellini, Multivariate moment type operators: approximation properties in Orlicz spaces. J. Math. Ineq. 2 (2008), 247-259. CR - C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini, A Korovkin theorem in multivariate modular function spaces. J. Func. Spaces Appl., 7 (2009), 105-120. CR - C. Bardaro, J. Musielak, G. Vinti, Nonlinear Integral Operators and Applications. De Gruyter Ser. Nonlinear Anal. Appl. 9, Walter de Gruyter, Berlin (2003). CR - 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. CR - C. Belen, M. Yildirim, Statistical approximation in multivariate modular function spaces. Comment. Math. 51 (2011), 39-53. CR - A. Boccuto, X. Dimitriou, Modular …lter convergence theorems for Urysohn integral operators and applications. Acta Math. Sinica, 29 (2013), 1055-1066. CR - J. Boos, Classical and Modern Methods in Summability. Oxford University Press (2000). CR - P. L. Butzer and H. Berens, Semi-groups of operators and approximation. Die Grundlehren der Mathematischen Wissenschaften, 145, Springer, New York, (1967). CR - A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32 (2002), 129-138. CR - S. Karakus, K. Demirci, O. Duman, Statistical approximation by positive linear operators on modular spaces. Positivity, 14 (2010), 321-334. CR - S. Karakus, K. Demirci, Matrix summability and Korovkin type approximation theorem on modular spaces. Acta Math. Univ. Commenianae, 2 (2010), 281-292. CR - P. P. Korovkin, Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi, (1960). CR - W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability. J. Math. Anal. Appl. (1989), 362-371. CR - J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer, Berlin (1983). CR - J. Musielak and W. Orlicz, On modular spaces. Studia Math. 18 (1959), 49-65. CR - U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods. J. Math. Anal. Appl. 238 (1999), 44-66. CR - 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. CR - Current address : Department of Mathematics, Hitit University, Çorum, Turkey E-mail address : tugbayurdakadim@hotmail.com UR - https://doi.org/10.1501/Commua1_0000000760 L1 - https://dergipark.org.tr/en/download/article-file/774168 ER -