Geodesic
Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p, q)-integrals
Filomat, Tome 36 (2022) no. 15, p. 5221

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

DOI

In this paper, Lupaş Bernstein-Kantorovich operators have been studied using Jackson and Riemann type (p, q)-integrals. It has been shown that (p, q)-integrals as well as Riemann type (p, q)-integrals are not well defined for 0 q p 1 and thus further analysis is needed. Throughout the paper, the case 1 ≤ q p ∞ has been used. Advantages of using Riemann type (p, q)-integrals are discussed over general (p, q)-integrals. Lupaş Bernstein-Kantorovich operators constructed via Jackson integral need not be positive for every f ≥ 0. So to make these operators based on general (p, q)-integral positive, one need to con- sider strictly monotonically increasing functions, and to handle this situation Lupaş Bernstein-Kantorovich operators are constructed using Riemann type (p,q)-integrals. However Lupaş (p,q)-Bernstein-Kantorovich operators based on Riemann type (p, q)-integrals are always positive linear operators. Approximation properties for these operators based on Korovkin’s type approximation theorem are investigated. The rate of convergence via modulus of continuity and function f belonging to the Lipschitz class is computed.
DOI : 10.2298/FIL2215221I
Classification : 65D17, 41A10, 41A25, 41A36
Keywords: (p, q)-integers, Lupaş (p, q)-Bernstein-Kantorovich operators, general (p, q)-integral, Riemann type (p, q)-integrals, modulus of continuity, Korovkin type approximation 
Mohammad Iliyas; Rameez A Bhatt; Asif Khan; M Mursaleen. Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p, q)-integrals. Filomat, Tome 36 (2022) no. 15, p. 5221 . doi: 10.2298/FIL2215221I
@article{10_2298_FIL2215221I,
     author = {Mohammad Iliyas and Rameez A Bhatt and Asif Khan and M Mursaleen},
     title = {Lupa\c{s} {Bernstein-Kantorovich} operators using {Jackson} and {Riemann} type (p, q)-integrals},
     journal = {Filomat},
     pages = {5221 },
     year = {2022},
     volume = {36},
     number = {15},
     doi = {10.2298/FIL2215221I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2215221I/}
}
TY  - JOUR
AU  - Mohammad Iliyas
AU  - Rameez A Bhatt
AU  - Asif Khan
AU  - M Mursaleen
TI  - Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p, q)-integrals
JO  - Filomat
PY  - 2022
SP  - 5221 
VL  - 36
IS  - 15
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2215221I/
DO  - 10.2298/FIL2215221I
LA  - en
ID  - 10_2298_FIL2215221I
ER  - 
%0 Journal Article
%A Mohammad Iliyas
%A Rameez A Bhatt
%A Asif Khan
%A M Mursaleen
%T Lupaş Bernstein-Kantorovich operators using Jackson and Riemann type (p, q)-integrals
%J Filomat
%D 2022
%P 5221 
%V 36
%N 15
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2215221I/
%R 10.2298/FIL2215221I
%G en
%F 10_2298_FIL2215221I

Cité par Sources :