TY - JOUR T1 - On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence AU - Taş, Emre AU - Yurdakadim, Tuğba PY - 2023 DA - June DO - 10.47000/tjmcs.1221861 JF - Turkish Journal of Mathematics and Computer Science JO - TJMCS PB - Matematikçiler Derneği WT - DergiPark SN - 2148-1830 SP - 180 EP - 183 VL - 15 IS - 1 LA - en AB - 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. KW - Korovkin type approximation KW - statistical convergence KW - positive linear operators CR - Altomare, F., Campiti, M., Korovkin Type Approximation Theory and Its Applications, De Gruyter Studies in Math., vol.17, de Gruyter&Co, Berlin, 1994. CR - Atlıhan, Ö.G., Orhan, C., Summation process of positive linear operators, Computers and Mathematics with Appl., 56(2008), 1188–1195. CR - Atlıhan, Ö.G., Ünver, M., Duman, O., Korovkin theorems on weighted spaces: revisited, Period. Math. Hungar., 75(2017), 201–209. CR - 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. CR - Connor, J.S., Two valued measures and summability, Analysis, 10(1990), 373–385. CR - Connor, J.S., R-type summability methods, Cauchy criteria, P-sets and statistical convergence, Proc. Amer. Math. Soc., 115(1992), 319–327. CR - Duman, O., Khan, M.K., Orhan, C., A-statistical convergence of approximating operators, Math. Inequal. Appl., 6(2003), 689–699. CR - Duman, O., Orhan, C., Statistical approximation by positive linear operators, Studia Math., 161(2004), 187–197. CR - Duman, O., Orhan, C., Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett., 18(2005), 1339–1344. CR - Duman, O. Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), 33–46. CR - Fast, H., Sur la convergence statistique, In Colloquium mathematicae, 2(1951), 241–244. CR - Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–314. CR - Fridy, J.A., Miller, H.I., Orhan, C., Statistical rates of convergence, Acta Sci. Math., 69(2003), 147–157. CR - 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. CR - Gadjiev, A.D., On P.P. Korovkin type theorems, Mat. Zametki, 20(1976), 781–786. CR - Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain Journal of Math., 32(2002), 129–137. CR - Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Doklady Akad. Nauk SSR., 90(1953), 961–964. CR - Miller, H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(1995), 1811–1819. CR - Popa, D., An operator version of the Korovkin theorem, J. Math. Anal. Appl., 515(2022), Article No: 126375. CR - Salat, T., On statistically convergent sequences of real numbers, Mat. Slovaca., 30(1980), 139–150. CR - 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. CR - Micchelli, C.A., Convergence of positive linear operators on C(X), J. Approx. Theory, 13(1975), 305–315. UR - https://doi.org/10.47000/tjmcs.1221861 L1 - https://dergipark.org.tr/en/download/article-file/2843205 ER -