85
Views
3
CrossRef citations to date
0
Altmetric
Articles

Blending type approximation by bivariate generalized Bernstein type operators

&
Pages 1449-1465 | Received 28 Feb 2019, Published online: 07 Aug 2019

References

  • T. Acar, A.M. Acu, and N. Manav, Approximation of functions by genuine Bernstein-Durrmeyer type operators, J. Math. Inequal 12(1) (2018), 975–987. doi: 10.7153/jmi-2018-12-74
  • T. Acar, A. Aral, and S.A. Mohiuddine, Approximation by bivariate (p, q)-Bernstein-Kantorovich operators, Iran. J. Sci. Technol. Trans. Sci. 42 (2018), 655–662. doi: 10.1007/s40995-016-0045-4
  • T. Acar and A. Kajla, Degree of approximation for bivariate generalized Bernstein type operators, Results Math. 73 (2018), 79, doi.org/10.1007/s00025-018-0838-1.
  • A.M. Acu, Stancu-Schurer-Kantorovich operators based on q−integers, Appl. Math. Comput. 259 (2015), 896–907.
  • P.N. Agrawal and N. Ispir, Degree of approximation for bivariate Chlodowsky-Szasz-Charlier type operators, Results Math. 69 (2016), 369–385. doi: 10.1007/s00025-015-0495-6
  • C. Badea, I. Badea, C. Cottin and H.H. Gonska, Notes on the degree of approximation of B−continuous and B-differentiable functions, Approx. Theory Appl. 4 (1988), 95–108.
  • C. Badea and C. Cottin, Korovkin-type theorems for Generalized Boolean Sum operators, Approximation Theory (Kecskemét, 1900), Vol. 58, pp. 51–68, Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, 1990.
  • D. Bărbosu, Bivariate operators of Schurer-Stancu type, An. Ştiinț, Univ. Ovidius Constanta Ser. Mat. 11 (2003), 1–8.
  • D. Bărbosu, Kantorovich-Stancu type operators, J. Inequal. Pure Appl. Math. 5 (2004), 1–6.
  • D. Bărbosu, Simultaneous approximation by bivariate Schurer-Stancu type operators, Math. Balkanica (N.S.) 20(3–4) (2006), 351–358.
  • D. Bărbosu and C.V. Muraru, Approximating B-continuous functions using GBS operators of Bernstein-Schurer-Stancu type based on q-integers, Appl. Math. Comput. 259 (2015), 80–87.
  • K. Bögel, Über die mehrdimensionale Differentiation, Jber. Deutsch. Math.-Verein. 65 (1962–1963), 45–71.
  • X. Chen, J. Tan, Z. Liu, and J. Xie, Approximation of functions by a new family of generalized Bernstein operators, J. Math. Anal. Appl. 450 (2017), 244–261. doi: 10.1016/j.jmaa.2016.12.075
  • O. Doǧru and V. Gupta, Korovkin-type approximation propeties of bivariate q-Meyer-König and Zeller operators, Calcolo 43 (2006), 51–63. doi: 10.1007/s10092-006-0114-8
  • H.H. Gonska, Quantitative Approximation in C(X), Habilitationsschrift, Universität Duisburg, Germany, 1985.
  • H. Gonska, M. Heilmann, and I. Rasa, Kantorovich operators of order k, Numer. Funct. Anal. Optim. 32 (2011), 717–738. doi: 10.1080/01630563.2011.580877
  • P. Gupta and P.N. Agrawal, Quantitative Voronovskaja and Grüss Voronovskaja-type theorems for operators of Kantorovich type involving multiple Appell polynomials, Iran. J. Sci. Technol. Trans. Sci. (2018), https://doi.org/10.1007/s40995-018-0613-x.
  • N. Ispir and I. Büyükyazici, Quantitative estimates for a certain bivariate Chlodowsky-Szasz-Kantorovich type operators, Math. Commun. 21 (2016), 31–44.
  • A. Kajla and T. Acar, Blending type approximation by generalized Bernstein-Durrmeyer type operators, Miskolc Math. Notes 19 (2018), 319–336. doi: 10.18514/MMN.2018.2216
  • A. Kajla and A.M. Acu, Blending type approximation by generalized Bernstein operators, (2019), submitted.
  • A. Kajla, N. Ispir, P.N. Agrawal, and M. Goyal, q-Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables, Appl. Math. Comput. 275 (2016), 372–385.
  • A. Kajla and D. Miclăuş, Blending type Approximation by GBS operators of generalized Bernstein-Durrmeyer type, Results Math. 73(1) (2018), doi.org/10.1007/s00025-018-0773-1.
  • M.A. Özarslan and T. Vedi, Direct and inverse theorems for multivariate Bernstein-Schurer-Stancu operators, Miskolc Math. Notes 16 (2015), 1073–1089. doi: 10.18514/MMN.2015.1209
  • R. Ruchi, B. Baxhaku, and P.N. Agrawal, GBS operators of bivariate Bernstein-Durrmeyer-Type on a triangle, Math. Methods Appl. Sci. 41(7) (2018), 2673–2683. doi: 10.1002/mma.4771
  • D.D. Stancu, The remainder in the approximation by a generalized Bernstein operator: a representation by a convex combination of second-order divided differences, Calcolo 35 (1998), 53–62. doi: 10.1007/s100920050008

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.