Approximation Results on an Infinite Interval Based on Power Series Statistical Sense

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.