Geodesic
Saturation and Inverse Theorems for Combinations of a Class of Exponential-Type Operators
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1224-1250

Voir la notice de l'article provenant de la source Cambridge University Press

Rates of convergence, saturation theorems and the socalled “inverse problems” for Bernstein polynomials have been intensively studied (see, e.g., [1 ; 4; 8; 14; 17]). The same problems for some other positive operators have also been investigated by many authors. In this paper, we shall use a uniform approach to study the saturation and inverse problems for a class of linear combinations of operators including Bernstein polynomials, and Szâsz, Post-Widder, Gauss-Weierstrass and Baskakov operators. 
May, C. P. Saturation and Inverse Theorems for Combinations of a Class of Exponential-Type Operators. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1224-1250. doi: 10.4153/CJM-1976-123-8
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[1] 1. Baisanski, B. and Bojanic, R., A note on approximation by Bernstein polynomials, Bull. A.M.S. 70 (1964), 675–677. Google Scholar

[2] 2. Baskakov, V. A., An example of a sequence of linear positive operators in the space of continuous functions (Russian), Doklady Akad. Nauk, 113 (1957), 249–251. Google Scholar

[3] 3. Berens, H., Pointwise saturation of positive operators, J. Approximation Theory, 6 (1972), 135–146. Google Scholar

[4] 4. Berens, H. and Lorentz, G. G., Inverse theorem for Bernstein polynomials, Indiana University Mathematics Journal, 21 (1972), 693–708. Google Scholar

[5] 5. Berezin, I. S. and Zhidkov, N. P., Computing methods, Vol. 1 (Pergamon Press, 1965, English Translation). Google Scholar

[6] 6. Butzer, P. L., Linear combinations of Bernstein polynomials, Can. J. Math. 5 (1953), 559- 567. Google Scholar

[7] 7. Butzer, P. L. and Berens, H., Semi-groups of operators and approximation (Springer-Verlag, New York Inc. 1967). Google Scholar

[8] 8. de Leeuw, K., On the degree of approximation by Bernstein polynomials, J. d'Anal. Math. 7 (1959), 89–104. Google Scholar

[9] 9. Ditzian, Z. and May, C. P., A saturation result for combinations of Bernstein polynomials, to appear, Tôhoku Math. J. Google Scholar

[10] 10. Dunford, N. and Schwartz, J., Linear operators, Part I: General theory (Interscience, New York 1958). Google Scholar

[11] 11. Frentiu, M., Linear combinations of Bernstein polynomials and of Mirakjan operators, (Romanian) Studia Univ. Babes-Bolyai Ser. Math.-Mech. 15 (1970), 63–68. Google Scholar

[12] 12. Lorentz, G. G., Approximation of functions (Holt, Rinehart and Winston 1966). Google Scholar

[13] 13. Lorentz, G. G., Bernstein polynomials (University of Toronto Press, Toronto 1953). Google Scholar

[14] 14. Lorentz, G. G., Inequalities and the saturation class for Bernstein polynomials, Proceedings of the conference at Oberwolfach on approximation theory, 1963 (Berkhauser Verlag, 1964). Google Scholar

[15] 15. Popoviciu, T., Sur Vapproximation des fonctions convexes d'ordre supérieur, Mathematica (Cluj), 10 (1935), 49–54. Google Scholar

[16] 16. Suzuki, Y., Saturation of local approximation by linear positive operators, Tôhoku Math. J. 17 (1965), 210–220. Google Scholar

[17] 17. Suzuki, Y., Saturation of local approximation by linear positive operators of Bernstein type, Tôhoku Math. J. 19 (1967), 429–453. Google Scholar

[18] 18. Suzuki, Y. and Watanabe, S., Some remarks on saturation problems in the local approximation II, Tôhoku Math. J. 21 (1969), 65–83. Google Scholar

[19] 19. Szâsz, O., Generalization of S. Bernstein s polynomials to the infinite interval, J. Research Nat. Bur. Standards 45 (1950), 239–245. Google Scholar

[20] 20. Timan, A. F., Theory of approximation of functions of a real variable, English translation (Pergamon Press, 1963). Google Scholar

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