TY - JOUR
T1 - Statistical Convergence of Szász-Mirakjan-Kantorovich-Type Operators and their Bivariate Extension
AU - Yadav, Rishikesh
AU - Mishra, Vishnu Narayan
AU - Meher, Ramakanta
AU - Mursaleen, M.
N1 - Publisher Copyright:
© 2022, University of Nis. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Our main aim is to investigate the approximation properties of the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of approximation is determined. Also using the weight function, the weighted statistical convergence theorem with the help of the Korovkin theorem is obtained. The statistical rate of convergence in the terms of modulus of continuity and function belonging to the Lipschitz class is determined. To support the convergence results of the proposed operators to the function, graphical representations take place and a comparison is shown with Szász-Mirakjan-Kantorovich operators through examples. The last section deals with, a bivariate extension of the proposed operators to determine the approximation of the function of two variables, additionally, the rate of convergence is estimated as well as the convergence of the bivariate operators is shown by graphical representations.
AB - Our main aim is to investigate the approximation properties of the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of approximation is determined. Also using the weight function, the weighted statistical convergence theorem with the help of the Korovkin theorem is obtained. The statistical rate of convergence in the terms of modulus of continuity and function belonging to the Lipschitz class is determined. To support the convergence results of the proposed operators to the function, graphical representations take place and a comparison is shown with Szász-Mirakjan-Kantorovich operators through examples. The last section deals with, a bivariate extension of the proposed operators to determine the approximation of the function of two variables, additionally, the rate of convergence is estimated as well as the convergence of the bivariate operators is shown by graphical representations.
KW - Korovkin-type approximation results
KW - modulus of continuity
KW - statistical convergence
KW - Szász-Mirakjan operators
KW - Szász-Mirakjan-Kantorovich operators
KW - weighted modulus of continuity
UR - http://www.scopus.com/inward/record.url?scp=85146258373&partnerID=8YFLogxK
U2 - 10.2298/fil2217895y
DO - 10.2298/fil2217895y
M3 - Article
AN - SCOPUS:85146258373
SN - 0354-5180
VL - 36
SP - 5895
EP - 5912
JO - Filomat
JF - Filomat
IS - 17
ER -