Kantorovich operators of order k

Numerical Functional Analysis and Optimization

Volumn 32, Issue 7, 2011, Pages 717-738

  Gonska, Heiner ^a   Heilmann, Margareta ^b   Raşa, Ioan ^c  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF WUPPERTAL   (Germany)

^c TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Bernstein operators; Degree of approximation; First and second order moduli of continuity; Kantorovich operators (of higher order); Positive linear operators; Simultaneous approximation; Voronovskaya's theorem

Indexed keywords

BERNSTEIN OPERATOR; DEGREE OF APPROXIMATION; FIRST AND SECOND ORDER MODULI OF CONTINUITY; KANTOROVICH OPERATORS (OF HIGHER ORDER); POSITIVE LINEAR OPERATORS; SIMULTANEOUS APPROXIMATION; VORONOVSKAYA'S THEOREM;

MATHEMATICAL OPERATORS;

EID: 79957610577     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630563.2011.580877     Document Type: Article

References (25)

1. H. Berens, and R.A. DeVore (1976). Quantitative Korovkin theorems for Lp-spaces. In: Approximation Theory II, Proceedings of the International Symposium. Austin, TX, pp. 289-298.
2. Yu.A. Brudnyj (1955). On a method for approximation of bounded functions given on an interval. Issled. Sovrem. Probl. Konstr. Teor. Funkts., Baku 40-45. (in Russian)
3. P.L. Butzer (1955). Summability of generalized Bernstein polynomials. I. Duke Math. J. 22:617-623.
4. M. Campiti (2000). Binomial-type coeffcients and classical approximation processes. In: Handbook of Analytic - Computational Methods in Applied Mathematics (G. Anastassiou, Ed.). Boca Raton, FL: Chapman & Hall, pp. 947-996.
5. G. Freud (1967). On approximation by positive linear methods. I, II. Stud. Sci. Math. Hung. 2:63-66. [3:365-370 (1968)]
6. M. Floater (2005). On the convergence of derivatives of Bernstein approximation. J. Approx. Theory 134:130-135. (Pubitemid 40595452)
7. H.H. Gonska (1979). Quantitative Aussagen zur Approximation Durch Positive Lineare Operatoren. Doctoral Dissertation. University of Duisburg.
8. H.H. Gonska (1984). Quantitative Korovkin-type theorems on simultaneous approximation. Math. Z. 186:419-433.
9. H. Gonska, M. Heilmann, and I. Ra̧sa (2010). Asymptotic behaviour of differentiated Bernstein polynomials revisited. General Mathematics (Sibiu) 18:45-53.
10. H. Gonska and R. P̌alťanea (2010). General Voronovskaya and asymptotic theorems in simultaneous approximation. Mediterr. J. Math. 7:37-49.
11. H. Gonska and I. Ra̧sa (2009). A Voronovskaya estimate with second order modulus of smoothness. In: Mathematical Inequalities (Proceedings of the 5th International Symposium, Sibiu 2008) (D. Acu et al., Eds.). Publishing House of "Lucian Blaga" University, Sibu, pp. 76-90.
12. H. Gonska and I. Ra̧sa (2009). Asymptotic behaviour of differentiated Bernstein polynomials. Mat. Vesnik 61:53-60.
13. H.W. Gould (1972). Combinatorial Identities. A Standardized Set of Tables Listing 500 Binomial Coefficient Summations. Henry W. Gould: Morgantown, WV.
14. D. Kacs(2008). Certain Bernstein-Durrmeyer Operators Preserving Linear Functions. Habilitationsschrift, University of Duisburg-Essen.
15. L.V. Kantorovich (1930). Sur certains developpements suivant les polynomes de la forme de S. Bernstein. I, II. C. R. Acad. Sci. USSR A 563-568:595-600.
16. R.P. Kelisky and T.J. Rivlin (1967). Iterates of Bernstein polynomials. Pacific J. Math. 21(3): 511-520.
17. H.-B. Knoop and P. Pottinger (1976). Ein Satz vom Korovkin-Typ fur Ck-Raume. Math. Z. 148:23-32.
18. A.J. Ĺpez-Moreno, J. Mart́́z-Moreno, and F.J. Munoz-Delgado (2003). Asymptotic behavior of Kantorovich type operators. Monografas del Semin. Matem. Garca de Galdeano 27:399-404.
19. G.G. Lorentz (1953). Bernstein Polynomials. University Press, Toronto.
20. J. Nagel (1983). Kantorovich operators of second order. Monatsh. Math. 95:33-44.
21. R. P̌alťanea (2003). Optimal constant in approximation by Bernstein operators. J. Comput. Anal. Appl. 5:195-235. (Pubitemid 36370573)
22. R. P̌alťanea (2004). Approximation Theory Using Positive Linear Operators. Birkhauser, Boston.
23. Bl. Sendov and V. Popov (n.d.). Konvergenz von Ableitungen linearer Operatoren. Handwritten German translation of notes used by the authors at the "Seminar on Interpolation and Convexity," Cluj-Napoca, September 1-10, 1968.
24. Bl. Sendov, and V. Popov (1969). The convergence of the derivatives of positive linear operators. C. R. Acad. Bulgare Sci. 22:507-509. (in Russian)
25. Bl. Sendov and V. Popov (1970). Convergence of the derivatives of positive linear operators. B'lgar. Akad. Nauk. Otdel. Mat. Fiz. Nauk. Izv. Mat. Inst. 11:107-115. (in Bulgarian)