The Rate of Convergence for Linear Shape-Preserving Algorithms
Dmitry Boytsov; Sergei Sidorov
Concrete Operators (2015)
- Volume: 2, Issue: 1, page 139-145, electronic only
- ISSN: 2299-3282
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] Barnabas B., Coroianu L., Gal Sorin G., Approximation and shape preserving properties of the Bernstein operator of maxproduct kind, Int. J. of Math. and Math., 2009, Article ID 590589, 1–26 Zbl1188.41016
- [2] Boytsov D. I., Sidorov S. P., Linear approximation method preserving k-monotonicity, Siberian electronic mathematical reports, 2015, 12, 21–27
- [3] Cárdenas-Morales D., Garrancho P., Rasa I., Bernstein-type operators which preserve polynomials, Comput. Math. Appl., 2011, 62, 158–163 [WoS] Zbl1228.41019
- [4] Cárdenas-Morales D., Muñoz-Delgado F. J., Improving certain Bernstein-type approximation processes, Mathematics and Computers in Simulation, 2008, 77, 170–178 Zbl1142.41302
- [5] Cárdenas-Morales D., Muñoz-Delgado F. J., Garrancho P., Shape preserving approximation by Bernstein-type operators which fix polynomials, Applied Mathematics and Computation, 2006, 182, 1615–1622 Zbl1136.65018
- [6] Floater M. S., On the convergence of derivatives of Bernstein approximation, J. Approx. Theory, 2005, 134, 130–135 [Crossref] Zbl1068.41010
- [7] Gal Sorin G., Shape-Preserving Approximation by Real and Complex Polynomials, Springer, 2008 Zbl1154.41002
- [8] Gonska H. H., Quantitative Korovkin type theorems on simultaneous approximation, Mathematische Zeitschrift, 1984, 186 (3), 419–433 Zbl0523.41013
- [9] Knoop H.-B., Pottinger P., Ein satz vom Korovkin-typ fur Ck raume, Math. Z., 1976, 148, 23–32 Zbl0322.41016
- [10] Kopotun K. A., Leviatan D., Prymak A., Shevchuk I. A., Uniform and pointwise shape preserving approximation by algebraic polynomials, Surveys in Approximation Theory, 2011, 6, 24–74 Zbl1296.41001
- [11] Kopotun K., Shadrin A., On k-monotone approximation by free knot splines, SIAM J. Math. Anal., 2003, 34, 901–924 Zbl1031.41007
- [12] Korovkin P. P., On the order of approximation of functions by linear positive operators, Dokl. Akad. Nauk SSSR, 1957, 114 (6), 1158–1161 (in Russian) Zbl0084.06104
- [13] Kvasov B. I., Methods of shape preserving spline approximation, Singapore: World Scientific Publ. Co. Pte. Ltd., 2000 Zbl0960.41001
- [14] Muñoz-Delgado F. J., Cárdenas-Morales D., Almost convexity and quantitative Korovkin type results, Appl.Math. Lett., 1998, 94 (4), 105–108 [Crossref] Zbl0942.41013
- [15] Muñoz-Delgado F. J., Ramírez-González V., Cárdenas-Morales D., Qualitative Korovkin-type results on conservative approximation, J. Approx. Theory, 1998, 94, 144–159 Zbl0911.41015
- [16] Pál J., Approksimation of konvekse funktioner ved konvekse polynomier, Mat. Tidsskrift, 1925, B, 60–65 Zbl51.0210.02
- [17] Popoviciu T., About the Best Polynomial Approximation of Continuous Functions. Mathematical Monography. Sect. Mat. Univ. Cluj., 1937, fasc. III, (in Romanian) Zbl63.0959.03
- [18] Pˇaltˇanea R., A generalization of Kantorovich operators and a shape-preserving property of Bernstein operators, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, 2012, 5 (54), 65–68
- [19] Shisha O., Mond B., The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A., 1968, 60, 1196– 1200 Zbl0164.07102
- [20] Sidorov S. P., Negative property of shape preserving finite-dimensional linear operators, Appl.Math. Lett., 2003, 16 (2), 257– 261 [Crossref] Zbl1062.41018
- [21] Sidorov S. P., Linear relative n-widths for linear operators preserving an intersection of cones, Int. J. of Math. and Math., 2014, Article ID 409219, 1–7 Zbl1310.41013
- [22] Sidorov S.P., On the order of approximation by linear shape-preserving operators of finite rank, East Journal on Approximations, 2001, 7 (1), 1–8 Zbl1085.41508