Geodesic
Statistical convergence of bivariate generalized Bernstein operators via four-dimensional infinite matrices
Filomat, Tome 36 (2022) no. 2, p. 507

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Our main aim in this work is to construct an original extension of bivariate Bernstein type operators based on multiple shape parameters to give an application of four-dimensional infinite matrices to approximation theory, and prove some Korovkin theorems using two summability methods: a statistical convergence method which is stronger than the classical case and a power series method. We obtain the rate of generalized statistical convergence, and the rate of convergence for the power series method. Moreover, we provide some computer graphics to numerically analyze the efficiency and accuracy of convergence of our operators and obtain corresponding error plots. All the results that have been obtained in the present paper can be extended to the case of n-variate functions
DOI : 10.2298/FIL2202507O
Classification : 41A10, 41A25, 41A36, 26A16, 40C05
Keywords: Multiple shape parameters, power series method, four-dimensional summability method, Robinson-Hamilton conditions, bivariate Bernstein operators, computer graphics 
Faruk Özger; Khursheed J Ansari. Statistical convergence of bivariate generalized Bernstein operators via four-dimensional infinite matrices. Filomat, Tome 36 (2022) no. 2, p. 507 . doi: 10.2298/FIL2202507O
@article{10_2298_FIL2202507O,
     author = {Faruk \"Ozger and Khursheed J Ansari},
     title = {Statistical convergence of bivariate generalized {Bernstein} operators via four-dimensional infinite matrices},
     journal = {Filomat},
     pages = {507 },
     year = {2022},
     volume = {36},
     number = {2},
     doi = {10.2298/FIL2202507O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2202507O/}
}
TY  - JOUR
AU  - Faruk Özger
AU  - Khursheed J Ansari
TI  - Statistical convergence of bivariate generalized Bernstein operators via four-dimensional infinite matrices
JO  - Filomat
PY  - 2022
SP  - 507 
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2202507O/
DO  - 10.2298/FIL2202507O
LA  - en
ID  - 10_2298_FIL2202507O
ER  - 
%0 Journal Article
%A Faruk Özger
%A Khursheed J Ansari
%T Statistical convergence of bivariate generalized Bernstein operators via four-dimensional infinite matrices
%J Filomat
%D 2022
%P 507 
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2202507O/
%R 10.2298/FIL2202507O
%G en
%F 10_2298_FIL2202507O

Cité par Sources :