Approximation by positive operators in the space \(C^{(p)}([a,b])\)
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Francesco Altomare, Positive linear forms and their determining subspaces. Ann. Mat. Pura Appl. (4) 154 (1989), 243-258,MR1043074, https://doi.org/10.1007/bf01790351
F. Altomare, Approximation of finitely defined operators in function spaces. Note Mat. 7 (1987), no. 2, 211-229 (1988), MR1016112.
Heinz Bauer, Gottlieb Leha, Susanne Papadopoulou, Determination of Korovkin closures. Math. Z. 168 (1979), no. 3, 263-274, MR0544594, https://doi.org/10.1007/bf01214516
H. Berens, G. G. Lorentz, Geometric theory of Korovkin sets. J. Approximation Theory 15 (1975), no. 3, 161-189, MR0390599, https://doi.org/10.1016/0021-9045(75)90100-8
T. K. Boehme, A. M. Bruckner, Functions with convex means. Pacific J. Math. 14 1964 1137-1149, MR0174673, https://doi.org/10.2140/pjm.1964.14.1137
Bruno Brosowski, A Korovkin-type theorem for differentiable functions. Approximation theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980), pp. 255-260, Academic Press, New York-London, 1980, MR0602724.
Campiti, M. Determining subspaces for continuous positive discrete linear forms, to appear in Ricerche di Matematica, 1989.
H. Esser, On pointwise convergence estimates for positive linear operators on C[a,b]. Nederl. Akad. Wetensch. Proc. Ser. A 79-Indag. Math. 38 (1976), no. 3, 189-194, MR0404941.
Gonska, H. H. Quantitative Aussagen zur Approximation durch positive lineare Operatoren, Disseration, Universität Duisburg, 1979 (in German).
Hans-Bernd Knoop, Peter Pottinger, Ein Satz vom Korovkin-Typ für Ck-Räume. (German) Math. Z. 148 (1976), no. 1, 23-32, MR0415168, https://doi.org/10.1007/bf01187866
G.I. Kudrjavcev, The convergence of sequences of linear operators to derivatives. (Russian) Proceedings of the Central Regional Union of Mathematical Departments, No. 1: Functional Analysis and Function Theory (Russian), pp. 122-136. Kalinin. Gos. Ped. Inst., Kalinin, 1970, MR0291699.
C. A. Micchelli, Convergence of positive linear operators on C(X). Collection of articles dedicated to G. G. Lorentz on the occasion of his sixty-fifth birthday, III. J. Approximation Theory 13 (1975), 305-315 MR0382937, https://doi.org/10.1016/0021-9045(75)90040-4
R. M. Min'kova, The congruence of the derivatives of linear operators. (Russian) C. R. Acad. Bulgare Sci. 23 1970, 627-629, MR0282117.
C. Mocanu, Monotony of weight-means of higher order. Anal. Numér. Théor. Approx. 11 (1982), no. 1-2, 115-127,MR0692477.
Mocanu, C., Măsuri relativ invariante. Operatori de mediere, Teză de doctorat, Univ. Cluj-Napoca, 1982 (in Romanian).
M. Nicolescu, Ciprian Foiaş, Sur les moyennes généralisées successives d'une fonction. (French) Mathematica (Cluj) 4 (27) 1962 107-121, MR0155987.
Pottinger, P., Zur linearen Approximation im Raum Ck(I), Habilitationsschrift, Gesamthochschule Duisburg, 1976.
I. Raşa, Sur les fonctionnelles de la forme simple au sens de T. Popoviciu. (French) [On the functionals of simple form in the sense of T. Popoviciu] Anal. Numér. Théor. Approx. 9 (1980), no. 2, 261-268 (1981),MR0651782.
Helmut H. Schaefer, Banach lattices and positive operators. Die Grundlehren der mathematischen Wissenschaften, Band 215. Springer-Verlag, New York-Heidelberg, 1974. xi+376 pp, MR0423039.
BI. Sendov, V. Popov, The convergence of the derivatives of positive linear operators. (Russian) C. R. Acad. Bulgare Sci. 22 1969 507-509, MR0251415.
Stadler, S., Über 1-positive operatoren, Linear Operators and Approximation II (Proc. Conf. Oberwolfach Math. res. Inst. Oberwolfach, 1974), 00.391-403, Internat. Ser. Numer. Math. Vol.25, Birkhäuser, Basel, 1974.
A. A. Vasil'čenko, Korovkin systems in some function spaces. (Russian) Studies in functional analysis (Russian), pp. 6-14, i, Ural. Gos. Univ., Sverdlovsk, 1978, MR0559714.
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