1Department of Mathematics, Govt. General Degree College at Manbazar II, West Bengal, India 2Garfa D.N.M. Girls High School, Kolkata, West Bengal, India
Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 1, pp. 131-142
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Sudipta Dutta; Rima Ghosh; Sudipta Dutta; Rima Ghosh. Korovkin type approximation theorem on an infinite interval in $A^{\mathcal{I}}$-statistical sense. Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 1, pp. 131-142. http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a12/
@article{AMUC_2020_89_1_a12,
author = {Sudipta Dutta and Rima Ghosh and Sudipta Dutta and Rima Ghosh},
title = { Korovkin type approximation theorem on an infinite interval in $A^{\mathcal{I}}$-statistical sense},
journal = {Acta mathematica Universitatis Comenianae},
pages = {131--142},
year = {2020},
volume = {89},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a12/}
}
TY - JOUR
AU - Sudipta Dutta
AU - Rima Ghosh
AU - Sudipta Dutta
AU - Rima Ghosh
TI - Korovkin type approximation theorem on an infinite interval in $A^{\mathcal{I}}$-statistical sense
JO - Acta mathematica Universitatis Comenianae
PY - 2020
SP - 131
EP - 142
VL - 89
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a12/
ID - AMUC_2020_89_1_a12
ER -
%0 Journal Article
%A Sudipta Dutta
%A Rima Ghosh
%A Sudipta Dutta
%A Rima Ghosh
%T Korovkin type approximation theorem on an infinite interval in $A^{\mathcal{I}}$-statistical sense
%J Acta mathematica Universitatis Comenianae
%D 2020
%P 131-142
%V 89
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a12/
%F AMUC_2020_89_1_a12
In this paper we consider the notion of AI-statistical convergence forreal sequences and establish a Korovkin type approximation theorem for positive linear operators on $UC*[0,\infty)$, the Banach space of all real valued uniform continuous functions on [0,\infty)$ with the property that $\displaystyle{\lim_{x\rightarrow \infty}f(x)}$ exists finitely for any $f\in UC_{*}[0,\infty)$. We then construct an example which shows that our new result is stronger than its classical version. In the last section, we extend the Korovkin type approximation theorem for positive linear operators on $UC_{*}\left([0,\infty)\times[0,\infty)\right)$.
