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Approximation by Stancu-Chlodowsky type lambda-Bernstein operators

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Warianty tytułu
Języki publikacji
EN
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EN
In this paper,we give some approximation properties by Stancu-Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.
Wydawca
Rocznik
Strony
97--110
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
  • Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
  • Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
  • Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
  • Department of Mathematics, Dhamar University, Dhamar, Yemen
autor
  • Math and Science Department, Community College of Qatar, P.O.Box 7344, Doha, Qatar
Bibliografia
  • [1] S. N. Bernstein, Démonstration du théoréme de Weierstrass fondée sur la calcul des probabilités, Comm. Soc. Math. Charkow Sér. 13 (1912), 1-2.
  • [2] I. Büyükyazici, On the approximation properties of two-dimensional q-Bernstein-Chlodowsky polynomials, Math. Commun. 14 (2009), no. 2, 255-269.
  • [3] I. Büyükyazici and E. İbikli, Inverse theorems for Bernstein-Chlodowsky type polynomials, J. Math. Kyoto Univ. 46 (2006), no. 1, 21-29.
  • [4] Q.-B. Cai, B.-Y. Lian and G. Zhou, Approximation properties of λ-Bernstein operators, J. Inequal. Appl. 2018 (2018), Paper No. 61.
  • [5] I. Chlodovsky, Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M. S. Bernstein, Compos. Math. 4 (1937), 380-393.
  • [6] R. A. DeVore and G. G. Lorentz, Constructive Approximation, Grundlehren Math. Wiss. 303, Springer, Berlin, 1993.
  • [7] A. D. Gadjiev, R. O. Efendiev and E. Ibikli, Generalized Bernstein-Chlodowsky polynomials, Rocky Mountain J. Math. 28 (1998), no. 4, 1267-1277.
  • [8] E. A. Gadjieva and T. K. Gasanova, Approximation by two dimensional Bernstein-Chlodowsky polynomials in triangle with mobile boundary, Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 20 (2000), no. 4, 47-51.
  • [9] E. A. Gadjieva and E. Ibikli, Weighted approximation by Bernstein-Chlodowsky polynomials, Indian J. Pure Appl. Math. 30 (1999), no. 1, 83-87.
  • [10] A. D. Gadžiev, A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin’s theorem (in Russian), Dokl. Akad. Nauk SSSR 218 (1974), 1001-1004; translation in Sov. Math. Dokl. 15 (1974), no. 5, 1433-1436.
  • [11] E. İbikli, On Stancu type generalization of Bernstein-Chlodowsky polynomials, Mathematica 42(65) (2000), no. 1, 37-43.
  • [12] M. Mursaleen, A. A. H. Al-Abied and A. Alotaibi, On (p, q)-Szász-Mirakyan operators and their approximation properties, J. Inequal. Appl. 2017 (2017), Paper No. 196.
  • [13] M. Mursaleen, K. J. Ansari and A. Khan, Corrigendum to: “Some approximation results by (p, q)-analogue of Bernstein-Stancu operators” [Appl. Math. Comput. 264(2015) 392-402] [MR3351620], Appl. Math. Comput. 269 (2015), 744-746.
  • [14] M. Mursaleen, K. J. Ansari and A. Khan, On (p, q)-analogue of Bernstein operators, Appl. Math. Comput. 266 (2015), 874-882; erratum, Appl. Math. Comput. 278 (2015), 70-71.
  • [15] M. Mursaleen, M. Nasiruzzaman, A. Khan and K. J. Ansari, Some approximation results on Bleimann-Butzer-Hahn operators defined by (p, q)-integers, Filomat 30 (2016), no. 3, 639-648.
  • [16] A. E. Piriyeva, On order of approximation of functions by generalized Bernstein-Chlodowsky polynomials, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 21 (2004), 157-164.
  • [17] S. Rahman, M. Mursaleen and A. M. Acu, Approximation properties of λ-Bernstein-Kantorovich operators with shifted knots, Math. Methods Appl. Sci. 42 (2019), no. 11, 4042-4053.
  • [18] T. Vedi and M. Ali Özarslan, Chlodowsky variant of q-Bernstein-Schurer-Stancu operators, J. Inequal. Appl. 2014 (2014), Article ID 189.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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