A NEW APPROACH IN OBTAINING A BETTER ESTIMATION IN APPROXIMATION BY POSITIVE LINEAR OPERATORS

Yıl 2009, Cilt: 58 Sayı: 1, 17 - 22, 01.02.2009

Ali Özarslan M. Oktay Duman

https://doi.org/10.1501/Commua1_0000000643

Cited By: 2

Öz

In this study, without preserving some test functions, we presenta new approach in obtaining a better error estimation in the approximationby means of positive linear operators. We also show that our method can beapplied to many well-known approximation operators

Anahtar Kelimeler

The Korovkin theorem, Bernstein polynomials, Szász-Mirakjan operators, Bernstein-Kantorovich operators, rate of convergence

Kaynakça

• O. Agratini, Linear operators that preserve some test functions. Int. J. Math. Math. Sci. Art.ID 94136 (2006), 11 pp.
• O. Agratini, On the iterates of a class of summation-type linear positive operators, Comput. Math. Appl. 55 (2008) 1178-1180.
• F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Application, Wal- ter de Gruyter Studies in Math. 17, de Gruyter & Co., Berlin, 1994.
• O. Duman and M.A. Özarslan, Szász-Mirakjan type operators providing a better error esti- mation, Appl. Math. Lett. 20 (2007) 1184-1188.
• J.P. King, Positive linear operators which preserve x2, Acta. Math. Hungar. 99 (2003) 203-208.
• P.P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, India, 1960.
• M.A. Özarslan and O. Duman, MKZ type operators providing a better estimation on [1=2; 1), Canadian Math. Bull. 50 (2007) 434-439. Current address : M. Ali Özarslan: Eastern Mediterranean University, Faculty of Arts and
• Sciences, Department of Mathematics, Gazimagusa, Mersin 10, Turkey
• Oktay Duman: TOBB Economics and Technology University, Faculty of Arts and Sciences, De
• partment of Mathematics, Sö¼gütözü 06530, Ankara, Turkey E-mail address : [e-mail], [e-mail]