An abstract version of the Korovkin approximation theorem

Publicationes Mathematicae Debrecen

Volumn 69, Issue 1-2, 2006, Pages 33-46

  Duman, Oktay ^a,b,c   Orhan, Cihan ^a,b  

^a Ankara University ^*

^b ANKARA UNIVERSITY   (Turkey)

^c TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY   (Turkey)

Author keywords

A density; A statistical convergence; Positive linear operators; Statistical convergence; The Korovkin theorem

Indexed keywords

EID: 33746268574     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. F. ALTOMARE and M. CAMPITI, Korovkin Type Approximation Theory and Its Applications, de Gruyter Stud. Math. 17, de Gruyter, Berlin, 1994.
2. R. BOJANIC and F. CHENG, Estimates for the rate of approximation of functions of bounded variation by Hermite-Fejer polynomials, Proceedings of the conference of Canadian Math. Soc., Vol. 3, 1983, 5-17.
3. R. BOJANIC and M. K. KHAN, Summability of Hermite-Fejer interpolation for functions of bounded variation, J. Nat. Sci. Math. 32 (1992), 5-10.
4. J. Boos, Classical and Modern Methods in Summability, Oxford University Press, UK, 2000.
5. J. S. CONNOR, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull. 32 (1989), 194-198.
6. J. S. CONNOR, A topological and functional analytic approach to statistical convergence. Analysis of Divergence, (Orono, ME, 1997), Applied Numer. Harmon. Anal., Birkhäuser, Boston, MA, 1999, 403-413.
7. O. DUMAN, Statistical approximation for periodic functions, Demonstratio Math. 36 (2003), 873-878.
8. O. DUMAN and C. ORHAN, Statistical approximation in the space of locally integrable functions, Publ. Math. Debrecen 63 (2003), 133-144.
9. O. DUMAN, M. K. KHAN and C. ORHAN, A-Statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), 689-699.
10. O. DUMAN and C. ORHAN, Statistical approximation by positive linear operators, Studia Math. 161 (2004), 187-197.
11. H. FAST, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
12. A. R. FREEDMAN and J. J. SEMBER, Densities and summability, Pacific J. Math. 95 (1981), 293-305.
13. J. A. FRIDY, On statistical convergence, Analysis 5 (1985), 301-313.
14. J. A. FRIDY and C. ORHAN, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), 3625-3631.
15. A. D. GADJIEV and C. ORHAN, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
16. G. H. HARDY, Divergent Series, Oxford Univ. Press, London, 1949.
17. 2, Acta Math. Hungar. 99 (2003), 203-208.
18. E. KOLK, The statistical convergence in Banach spaces, Tartu Ül. Toimetised 928 (1991), 41-52.
19. E. KOLK, Matrix summability of statistically convergent sequences, Analysis 13 (1993), 77-83.
20. P. P. KOROVKIN, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
21. H. N. MHASKAR and D. V. PAI, Fundamentals of Approximation Theory, Alpha Science Int. Ltd., 2000.
22. H. I. MILLER, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811-1819.
23. H. STEINHAUS, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.