Year: 2026
Type: article
Abstract: This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any P-statistically convergent sequence contains a classically convergent subsequence over a density 1 set, which plays a foundational role in the analysis. As a conclusion, we investigate the convergence of the r-th order generalization of linear operators, which may lack positivity, and present a Korovkin-type approximation theorem for periodic functions, both utilizing P-statistical convergence. These contributions generalize and improve existing results in approximation theory, providing novel insights and methodologies, supported by practical examples and corollaries.
Authors: Dilek Söylemez, Mehmet Ünver
Institutions: Selçuk University, Ankara University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Selçuk Üniversitesi
OpenAlex ID: W4416711896