Approximation by means of piecewise linear functions

Results in Mathematics

Volumn 35, Issue 1-2, 1999, Pages 89-102

  Kacsó, Daniela P ^a  

^a TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Bernstein operators; positive linear operators; Stancu operators

Indexed keywords

EID: 0348168889     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322024     Document Type: Article

References (21)

1. H. Burkill: Cesàro—Perron almost periodic functions, Proc. London Math. Soc. (Series 3) 2 (1952), 150–174.
2. I. Gavrea, H.H. Gonska, D.P. Kacsó: Positive linear operators with equidistant nodes. Comput. Math. Appl. 32 (1996), 23–32.
3. I. Gavrea, H.H. Gonska, D.P. Kacsó: On discretely defined positive linear polynomial operators giving optimal degrees of approximation. To appear in “Rend. Circ. Mat. Palermo (2) Suppl.”. Temporary reference: Schriftenreihe des Fachbereichs Mathematik, Univ. Duisburg / Germany, SM-DU-364 (1996).
4. I. Gavrea, H.H. Gonska, D.P. Kacsó: On linear operators with equidistant nodes: negative results. To appear in “Rend. Circ. Mat. Palermo (2) Suppl.”. Temporary reference: Schriftenreihe des Fachbereichs Mathematik, Univ. Duisburg / Germany, SM-DU-346 (1996).
5. I. Gavrea, H.H. Gonska, D.P. Kacsó: Variation on Butzer’s problem: Characterization of the solutions. Comput. Math. Appl. 34 (1997), 51–64.
6. H.H. Gonska: Quantitative Aussagen zur Approximation durch positive lineare Operatoren. Dissertation, Univ. Duisburg 1979.
7. H.H. Gonska: Two problems on best constants in direct estimates, Problem Section of Proc. Edmonton Conf. Approximation Theory (ed. by Z. Ditzian et al.), 194. Providence, RI: Amer. Math. Soc. 1983.
8. H.H. Gonska: Quantitative Korovkin-type theorems on simultaneous approximation, Math. Z. 186 (1984), 419–433.
9. H.H. Gonska, J. Meier: Quantitative theorems on approximation by Bernstein-Stancu operators, Calcolo 21 (1984) 317–335.
10. H.H. Gonska, D.-x. Zhou: On an extremal problem concerning Bernstein operators, Serdica Math. J. 21 (1995), 137–150.
11. H.H. Gonska, X.-1. Zhou: Polynomial approximation with side conditions: recent results and open problems. In: Proc. of the First International Colloquium on Numerical Analysis (Plovdiv 1992, ed. by D. Bainov and V. Covachev), 61–71. Zeist/The Netherlands: VSP International Science Publishers 1993.
12. r[a,b]. Ph.D. Thesis, Cluj-Napoca: Babeş-Bolyai University 1997.
13. A. Lupaş: Contribuţii la teoria aproximării prin operatori liniari. Ph.D. Thesis, Cluj-Napoca: Babeş-Bolyai University 1975.
14. J. Meier: Zur Approximation durch gewöhnliche und modifizierte Bernstein-Operatoren unter besonderer Berücksichtigung quantitativer Aussagen und asymptotischer Formeln. Staatsexamensarbeit, Univ. Duisburg 1982.
15. R. Păltănea: Best constant in estimates with second order moduli of continuity. In: “Approximation Theory” (Proc. Int. Dortmund Meeting on Approximation Theory 1995; ed. by M.W. Müller et al.), 251–275. Berlin: Akad. Verlag 1995.
16. R. Păltănea: Optimal Estimates with moduli of continuity, Result. Math. 32 (1997), 318–331.
17. T. Popoviciu: Curs de Analiză Matematică, Partea III-a Continuitate. Cluj-Napoca: Babeş-Bolyai University 1974.
18. D.D. Stancu: Evaluation of the remainder term in approximation formulas by Bernstein polynomials, Math. Comp. 83 (1963), 270–278.
19. D.D. Stancu: Approximation of functions by means of some new classes of positive linear operators. In: “Numerische Methoden der Approximationstheorie” (Proc. Conf. Math. Res. Inst. Oberwolfach 1971; ed. by L. Collatz, G. Meinardus), 187–203. Basel: Birkhäuser 1972.
20. D.D. Stancu: Approximation properties of a class of multiparameter positive linear operators. In: “Approximation and Optimization” (Proc. of ICAOR 1996; ed. by D.D. Stancu, Gh. Coman, W. Breckner, P. Blaga), 107–120. Cluj-Napoca: Transilvania Press 1997.
21. H. Whitney: On functions with bounded n-th differences, J. Math. Pures et Appl. 36 (1957), 67–95.