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2015 | 2 | 1 |

Tytuł artykułu

The Rate of Convergence for Linear Shape-Preserving Algorithms

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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 maxproduct kind, 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 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]
  • [4] Cárdenas-Morales D., Muñoz-Delgado F. J., Improving certain Bernstein-type approximation processes, Mathematics and Computers in Simulation, 2008, 77, 170–178
  • [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
  • [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 algebraic polynomials, 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 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
  • [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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