This paper introduces a new approximation theorem, type of Korovkin, for positive linear operators (pLO) defined on the Banach space C∗ [0, ∞) comprising all real-valued continuous functions on [0, ∞) that converge to a finite limit as their argument approaches infinity. By applying statistical convergence with respect to power series methods and employing the test functions 1, exp(−u) and exp(−2u), we derive a novel approximation result. Our findings demonstrate that the proposed method outperforms classical and statistical approaches, as illustrated by a concrete example. Furthermore, we explore the rate of convergence associated with this new approximation theorem.
Approximation Results on an Infinite Interval Based on Power Series Statistical Sense
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Yıldız S., Demirci K., Dirik F. (2025) "Approximation Results on an Infinite Interval Based on Power Series Statistical Sense
" Dolomites Research Notes on Approximation, 18(2), 17-24. DOI: 10.25430/pupj-DRNA-2025-2-4
Year of Publication
2025
Journal
Dolomites Research Notes on Approximation
Volume
18
Issue Number
2
Start Page
17
Last Page
24
Date Published
03/2025
ISSN Number
2035-6803
Serial Article Number
4
DOI
10.25430/pupj-DRNA-2025-2-4
Issue
Section
Articles