The primary goal of this paper is to present the generalization of λ-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [
Citation: |
[1] |
A.-M. Acu, T. Acar and V. A. Radu, Approximation by modified Uρn operators, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113 (2019), 2715-2729.
doi: 10.1007/s13398-019-00655-y.![]() ![]() ![]() |
[2] |
A.-M. Acu, H. Gonska and I. Raşa, Grüss-type and Ostrowski-type inequalities in approximation theory, Ukr. Math. J., 63 (2011), 843-864.
doi: 10.1007/s11253-011-0548-2.![]() ![]() ![]() |
[3] |
A.-M. Acu, N. Manav and D. F. Sofonea, Approximation properties of λ-Kantorovich operators, J. Inequal. Appl., 2018 (2018), Paper No. 202, 12 pp.
doi: 10.1186/s13660-018-1795-7.![]() ![]() ![]() |
[4] |
P. N. Agrawal, Z. Finta and A. Sathish Kumar, Bivariate-q-Bernstein-Schurer-Kantorovich operators, Result Math., 67 (2015), 365-380.
doi: 10.1007/s00025-014-0417-z.![]() ![]() ![]() |
[5] |
M. Bodur, N. Manav and F. Tasdelen, Approximation properties of λ-Bernstein-Kantorovich-Stancu operators, Math. Slovaca, 72 (2022), 141-152.
doi: 10.1515/ms-2022-0010.![]() ![]() ![]() |
[6] |
Q.-B. Cai, The Bézier variant of Kantorovich type λ−Bernstein operators, J. Ineqal. Appl., (2018), Paper No. 90, 10 pp.
doi: 10.1186/s13660-018-1688-9.![]() ![]() ![]() |
[7] |
Q.-B. Cai, B. Y.- Lian and G. Zhou, Approximation properties of λ−Bernstein Operators, J. Ineqal. Appl., (2018).
![]() |
[8] |
Q.-B. Cai and G. Zhou, Blending type approximation by GBS operators of bivariate tensor product of lambda-Bernstein Kantorovich type, J. Inequal. Appl., (2018), Paper No. 268, 11 pp.
doi: 10.1186/s13660-018-1862-0.![]() ![]() ![]() |
[9] |
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.![]() ![]() ![]() |
[10] |
N. Deo and R. Pratap, α−Bernstein-Kantorovich operators, Afr. Mat., 31 (2020), 609-618.
doi: 10.1007/s13370-019-00746-4.![]() ![]() ![]() |
[11] |
R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.
![]() |
[12] |
Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, New York, 1987.
![]() |
[13] |
J. L. Durrmeyer, A Formula of Inversion of the Laplace Transform: Applications the Theory of Moments. Ph.D. Thesis, Faculty of Sciences of the University of Paris, 1967.
![]() |
[14] |
Z. Finta, Remark on Voronovaskaja theorem for q−Bernstein operators, Stud. Univ. Babes-Bolayai Math., 56 (2011), 335-339.
![]() ![]() |
[15] |
A. D. Gadzjiv, Theorems of the type of P.P. Korovkin type theorems, Math. Zametki, 20 (1976), 781-786; English Translation, Math Notes 20 (1976), 996-998.
![]() ![]() |
[16] |
S. G. Gal and V. Gupta, Approximation by certain integrated Bernstein-type operator in compct disks, Lobachevskii J. Math., 33 (2012), 39-46.
doi: 10.1134/S1995080212010040.![]() ![]() ![]() |
[17] |
H. Gonska and G. Tachev, Grüss-type inequalities for positive linear operators with second order moduli, Mat. Vesn., 63 (2011), 247-252.
![]() ![]() |
[18] |
V. Gupta and A. Aral, Bernstein-Durrmeyer operators based two parameters, Facta Univ. Ser. Math. Inform., 31 (2016), 79-95.
![]() ![]() |
[19] |
V. Gupta, G. Tachev and A.-M. Acu, Modified Kantorovich operators with better approximation properties, Numer. Algor., 81 (2019), 125-149.
doi: 10.1007/s11075-018-0538-7.![]() ![]() ![]() |
[20] |
H. S. Jung, N. Deo and M. Dhamija, Pointwise approximation by Bernstein type operators in mobile interval, Appl. Math. Comput., 244 (2014), 683-694.
doi: 10.1016/j.amc.2014.07.034.![]() ![]() ![]() |
[21] |
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.![]() ![]() ![]() |
[22] |
P. P. Korovkin, On convergence of linear positive operators in the space of continuous functions (Russian), Doklady Akad. Nauk. SSSR(NS), 90 (1953), 961-964.
![]() ![]() |
[23] |
A. Lupaş and D. H. Mache, Approximation by Vn−operators, Ergebnisbericht der lehrstuhle Ⅲ und Ⅷ der Universitat Dortmund 99, 1990.
![]() |
[24] |
D. H. Mache and D. X. Zhou, Characterization theorem for the approximation by a family of operators, J. Approx. Th., 84 (1996), 145-161.
doi: 10.1006/jath.1996.0012.![]() ![]() ![]() |
[25] |
F. Özger, Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators, Filomat, 33 (2019), 3473-3486.
doi: 10.2298/FIL1911473O.![]() ![]() ![]() |
[26] |
M. A. ¨Ozarslan and H. Aktuglu, Local approximation for certain King type operators., Filomat, 27 (2013), 173-181.
doi: 10.2298/FIL1301173O.![]() ![]() ![]() |
[27] |
R. Pǎltǎnea, Sur un operateur polynomial define sur I'ensemble des fonctions intergrables, Bebes-Bolyai Univ., Faculty of Maths, Research Seminar, 2 (1983), 101-106.
![]() ![]() |
[28] |
H. M. Srivastava, F. Özger and S. A. Mohiuddine, Construction of stancu-type bernstein operators based on Bézier bases with shape parameter λ, Symmetry, 11 (2019), 316.
![]() |