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Tytuł artykułu

The Rate of Convergence for Linear Shape-Preserving Algorithms

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove some results which give explicit methods for determining an upper bound for the rate of approximation by means of operators preserving a cone. Thenwe obtain some quantitative results on the rate of convergence for some sequences of linear shape-preserving operators.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-09-03
zaakceptowano
2015-11-18
online
2015-11-30
Twórcy
  • Saratov State University, 83, Astrakhanskaya Str., 410012 Saratov, Russia
  • Saratov State University, 83, Astrakhanskaya Str., 410012 Saratov, Russia
Bibliografia
  • [1] Barnabas B., Coroianu L., Gal Sorin G., Approximation and shape preserving properties of the Bernstein operator of maxproductkind, Int. J. of Math. and Math., 2009, Article ID 590589, 1–26
  • [2] Boytsov D. I., Sidorov S. P., Linear approximation method preserving k-monotonicity, Siberian electronic mathematicalreports, 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]
  • [4] Cárdenas-Morales D., Muñoz-Delgado F. J., Improving certain Bernstein-type approximation processes, Mathematics andComputers in Simulation, 2008, 77, 170–178
  • [5] Cárdenas-Morales D., Muñoz-Delgado F. J., Garrancho P., Shape preserving approximation by Bernstein-type operatorswhich fix polynomials, Applied Mathematics and Computation, 2006, 182, 1615–1622
  • [6] Floater M. S., On the convergence of derivatives of Bernstein approximation, J. Approx. Theory, 2005, 134, 130–135[Crossref]
  • [7] Gal Sorin G., Shape-Preserving Approximation by Real and Complex Polynomials, Springer, 2008
  • [8] Gonska H. H., Quantitative Korovkin type theorems on simultaneous approximation, Mathematische Zeitschrift, 1984, 186(3), 419–433
  • [9] Knoop H.-B., Pottinger P., Ein satz vom Korovkin-typ fur Ck raume, Math. Z., 1976, 148, 23–32
  • [10] Kopotun K. A., Leviatan D., Prymak A., Shevchuk I. A., Uniform and pointwise shape preserving approximation by algebraicpolynomials, Surveys in Approximation Theory, 2011, 6, 24–74
  • [11] Kopotun K., Shadrin A., On k-monotone approximation by free knot splines, SIAM J. Math. Anal., 2003, 34, 901–924
  • [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)
  • [13] Kvasov B. I., Methods of shape preserving spline approximation, Singapore: World Scientific Publ. Co. Pte. Ltd., 2000
  • [14] Muñoz-Delgado F. J., Cárdenas-Morales D., Almost convexity and quantitative Korovkin type results, Appl.Math. Lett., 1998,94 (4), 105–108[Crossref]
  • [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
  • [16] Pál J., Approksimation of konvekse funktioner ved konvekse polynomier, Mat. Tidsskrift, 1925, B, 60–65
  • [17] Popoviciu T., About the Best Polynomial Approximation of Continuous Functions. Mathematical Monography. Sect. Mat.Univ. Cluj., 1937, fasc. III, (in Romanian)
  • [18] Pˇaltˇanea R., A generalization of Kantorovich operators and a shape-preserving property of Bernstein operators, Bulletin ofthe 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
  • [20] Sidorov S. P., Negative property of shape preserving finite-dimensional linear operators, Appl.Math. Lett., 2003, 16 (2), 257–261[Crossref]
  • [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
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2015-0008
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