AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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Authors: SUDIPTA DUTTA, RIMA GHOSH.
DOI: 10.24193/subbmath.2020.2.06
Published Online: 2020-06-05
Published Print: 2020-06-30
pp. 243-254
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ABSTRACT: Following the notion of $A^mathcal{I}$-summability method for real sequences cite{espdsd2} we 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 $displaystyle{lim_{x ightarrow infty}f(x)}$ exists finitely for any $fin UC_{*}[0,infty)$. In the last section, we extend the Korovkin type approximation theorem for positive linear operators on $UC_{*}left([0,infty) imes[0,infty) ight)$. We then construct an example which shows that our new result is stronger than its classical version.
Key words: Positive linear operator, Korovkin type approximation theorem, ideal, AI-summable, AI2 -summable.
