This note discusses the indecomposability and decomposability of certain operators occurring frequently in approximation theory: piecewise linear interpolation and Bernsteintype operators. The second topic includes the central (absolute) moments of the composition of two operators and their asymptotic behavior.
Abel, U. and Heilmann, M., The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights, Mediterr. J. Math., 1 (2004), no. 4, 487–499. MR2005k:41075
Heilmann M. , 'The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights ' (2004 ) 1 Mediterr. J. Math. : 487 -499 .
Adell, J. A., Badía, F. G. and de la Cal, J., On the iterates of some Bernstein-type operators, J. Math. Anal. Appl., 209 (1997), no. 2, 529–541. MR98j:41021
Cal J. , 'On the iterates of some Bernstein-type operators ' (1997 ) 209 J. Math. Anal. Appl. : 529 -541 .
Altomare, F. and Campiti, M., Korovkin-type Approximation Theory and its Applications, Walter de Gruyter & Co., Berlin, 1994. MR95g:41001
Campiti M. , '', in Korovkin-type Approximation Theory and its Applications , (1994 ) -.
Derriennic, M. M., Sur l’approximation de fonctions intégrables sur [0, 1] par des polynômes de Bernstein modifiés, J. Approx. Theory, 31 (1981), no. 4, 325–343. MR82m:41004
Derriennic M. M. , 'Sur l’approximation de fonctions intégrables sur [0, 1] par des polynômes de Bernstein modifiés ' (1981 ) 31 J. Approx. Theory : 325 -343 .
Gonska, H., On the composition and decomposition of positive linear operators, in: Approximation Theory and its Applications (Ukrainian) (Kiev, 1999), 161–180, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 31, Kiev, 2000. MR2003g:41036
Gonska, H., Kacsó, D. and Raşa, I., On genuine Bernstein-Durrmeyer operators, Results Math., 50 (2007), no. 3–4, 213–225. MR2008f:41033
Raşa I. , 'On genuine Bernstein-Durrmeyer operators ' (2007 ) 50 Results Math. : 213 -225 .
Gonska, H. and Raşa, I., Asymptotic behaviour of differentiated Bernstein polynomials, Mat. Vesnik, 61 (2009), no. 1, 53–60.
Raşa I. , 'Asymptotic behaviour of differentiated Bernstein polynomials ' (2009 ) 61 Mat. Vesnik : 53 -60 .
Gonska, H. and Zhou, X.-l., The strong converse inequality for Bernstein-Kantorovich operators, Comput. Math. Appl., 30 (1995), no. 3–6, 103–128. MR96j:41011
Zhou X.-l. , 'The strong converse inequality for Bernstein-Kantorovich operators ' (1995 ) 30 Comput. Math. Appl. : 103 -128 .
Lupaş, A., Die Folge der Beta-Operatoren, Dissertation, Universität Stuttgart, 1972.
Lupaş, L. and Lupaş, A., Polynomials of binomial type and approximation operators, Studia Univ. Babeş-Bolyai Math., 32 (1987), no. 4, 61–69. MR90a:41020
Lupaş A. , 'Polynomials of binomial type and approximation operators ' (1987 ) 32 Studia Univ. Babeş-Bolyai Math. : 61 -69 .
Phelps, R. R., Lectures on Choquet’s Theorem, D. Van Nostrand, Princeton, N.J. et al., 1966. MR33#1690
Phelps R. R. , '', in Lectures on Choquet’s Theorem , (1966 ) -.