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A converse of asymptotic formulae in simultaneous approximation. (English) Zbl 1205.41016
Summary: In the general setting of simultaneous approximation by sequences of linear shape preserving operators, this paper contains a sort of converse result of Voronovskaya-type asymptotic formulae. As a by-product, a saturation result is derived. Applications to some very well-known approximation processes are also presented.
41A28Simultaneous approximation
[1]Abel, U.: Asymptotic approximation with Kantorovich polynomial, Approx. theory appl. 3, No. 14, 106-116 (1998) · Zbl 0919.41011
[2]Abel, U.; Ivan, M.: Asymptotic expansion of the jakimovski – leviatan operators and their derivatives, , 103-119 (2002) · Zbl 1039.41015
[3]Altomare, F.; Campiti, M.: Koronkin-type approximation theory and its applications, De gruyter studies in mathematics 17 (1994) · Zbl 0924.41001
[4]Amel’kovic&breve, V. G.; : A theorem converse to a theorem of voronovskaja type, Teor. funkc˘iı˘, funkc˘ional. Anal. i priloz˘en 2, 67-74 (1966)
[5]Bajsanski, B.; Bojanić, R.: A note on approximation by Bernstein polynomials, Bull. am. Math. soc. 70, 675-677 (1964) · Zbl 0122.30904 · doi:10.1090/S0002-9904-1964-11156-3
[6]Berens, H.: Pointwise saturation of positive operators, J. approx. Theory 6, 135-146 (1972) · Zbl 0262.41017 · doi:10.1016/0021-9045(72)90070-6
[7]Bonsall, F. F.: The characterization of generalized convex functions, Q. J. Math. Oxford ser. 2, No. 1, 100-111 (1950) · Zbl 0038.20903 · doi:10.1093/qmath/1.1.100
[8]Cárdenas-Morales, D.; Garrancho, P.; Muñoz-Delgado, F. J.: A result on asymptotic formulae for linear k-convex operators, Int. J. Differ. equ. Appl. 2, No. 3, 335-347 (2001) · Zbl 1040.41015
[9]Cárdenas-Morales, D.; Garrancho, P.: Local saturation of conservative operators, Acta math. Hungar. 100, No. 1 – 2, 83-95 (2003) · Zbl 1058.41017 · doi:10.1023/A:1024656217794
[10]Cárdenas-Morales, D.; Garrancho, P.; Muñoz-Delgado, F. J.: Addendum and corrigendum to ’local saturation of conservative operators’, Acta math. Hungar. 105, No. 3, 257-259 (2004) · Zbl 1133.41309 · doi:10.1023/B:AMHU.0000049292.17611.51
[11]D. Cárdenas-Morales and P. Garrancho, On saturation in conservative approximation, in: M. Gasca (Ed.), Multivariate Approximation and Interpolation with Applications, Monografıacute;as de la Academia de Ciencias de Zaragoza 20, Real Academia de Ciencias de Zaragoza, Zaragoza, 2002, pp. 59 – 67.
[12]Karlin, S. J.; Studden, W. J.: Tchebycheff systems, (1966)
[13]A.J. López-Moreno, Expresiones y estimaciones de operadores lineales conservativos, Ph.D. thesis, University of Jaén, Spain, 2001.
[14]López-Moreno, A. J.; Martı&acute, J.; Nez-Moreno; Muñoz-Delgado, F. J.: Asymptotic expression of derivatives of Bernstein type operators, Suppl. cir. Mat. Palermo ser. II 68, 615-624 (2002)
[15]López-Moreno, A. J.; Muñoz-Delgado, F. J.: Asymptotic expansion of multivariate conservative linear operators, J. comput. Appl. math. 150, 219-251 (2003) · Zbl 1025.41013 · doi:10.1016/S0377-0427(02)00661-1
[16]Lorentz, G. G.; Schumaker, L. L.: Saturation of positive operators, J. approx. Theory 5, 413-424 (1972) · Zbl 0233.41007 · doi:10.1016/0021-9045(72)90008-1
[17]Mühlbach, G.: Operatoren vom bernsteinschen typ, J. approx. Theory 3, 274-292 (1970)
[18]Pesin, I.: Classical and modern integration theories, (1951)
[19]Voronovskaya, E.: Détermination de la forme asymptotique d’approximation des fonctions par LES polynômes de S. Bernstein, Dokl. akad. Nauk. USSR, 79-85 (1932) · Zbl 0005.01205