Statistical approximation of Meyer-König and Zeller operators based on q-integers

Publicationes Mathematicae Debrecen

Volumn 68, Issue 1-2, 2006, Pages 199-214

  Dogru O ^a   Duman, O ^b  

^a ANKARA UNIVERSITY   (Turkey)

^b TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY   (Turkey)

Author keywords

A statistical convergence; Lipschitz type maximal function; Modulus of continuity; Positive linear operators; q integers; The Bohman Korovkin type theorem

Indexed keywords

EID: 33646064729     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. O. AGRATINI, Korovkin type error estimates for Meyer-König and Zeller operators, Math. Ineq. Appl. 4 (2001), 119-126.
2. J. A. H. ALKEMADE, The Second Moment for the Meyer-König and Zeller Operators, J. Approx. Theory 40 (1984), 261-273.
3. G. E. ANDREWS, R. ASKEY and R. ROY, Special Functions, Cambridge Univ. Press, 1999.
4. G. BLEIMANN, P. L. BUTZER and L. HAHN, A Bernstein-type operator approximating continuous functions on the semi axis, Proc. Netherl. Acad. Sci. A 83, Indag. Math. 42 (1980), 255-262.
5. E. W. CHENEY and A. SHARMA, Bernstein power series, Canad. J. Math. 16 (1964), 241-253.
6. K. DEMIRCI and C. ORHAN, Bounded multipliers of bounded A-statistically convergent sequences, J. Math. Anal. Appl. 235 (1999), 122-129.
7. K. DEMIRCI, M. K. KHAN and C. ORHAN, Strong and A-statistical comparisons for sequences, J. Math. Anal. Appl. 278 (2003), 27-33.
8. O. DOǦRU, On Bleimann, Butzer and Hahn type generalization of Blázs operators, Dedicated to Professor D. D. Stancu on his 75th birthday, Studia Univ. Babeş-Bolyai, Mathematica 47 (2002), 37-45.
9. O. DOǦRU, O. DUMAN and C. ORHAN, Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungar. 40 (2003), 359-371.
10. O. DUMAN, M. K. KHAN and C. ORHAN, A-Statistical convergence of approximating operators, Math. Ineq. Appl. 6 (2003), 689-699.
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, Lacunary statistical summability, J. Math. Anal. Appl. 173 (1993), 497-504.
15. J. A. FRIDY and C. ORHAN, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), 3625-3631.
16. A. D. GADJIEV and C. ORHAN, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
17. G. H. HARDY, Divergent Series, Oxford Univ. Press, London, 1949.
18. M. K. KHAN, On the rate of convergence of Bernstein power series for functions of bounded variation, J. Approx. Theory 57 (1989), 90-103.
19. E. KOLK, The statistical convergence in Banach spaces, Acta Et Commentationes Tartuensis 928 (1991), 41-52.
20. E. KOLK, Matrix summability of statistically convergent sequences, Analysis 13 (1993), 77-83.
21. B. LENZE, On Lipschitz type maximal functions and their smoothness spaces, Proc. Netherland Acad. Sci. A 91 (1998), 53-63.
22. W. MEYER-KÖNIG and K. ZELLER, Bernsteinsche potenzreihen, Studia Math. 19 (1960), 89-94.
23. H. I. MILLER, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811-1819.
24. G. M. PHILLIPS, On generalized Bernstein polynomials, Numerical Analysis: A.R. Mitchell 75th Birthday Volume, (G. A. Watson, ed.), World Science, Singapore, 1996, 263-269.
25. T. TRIF, Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numér. Théor. Approx. 29, no. 2 (2000), 221-229.