2025/09/02 by Dilek Söylemez, Söylemez, Dilek, Mehmet Ünver +1
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Fuzzy Systems and Optimization
paper · pdf · doi:10.48550/arxiv.2509.02557
openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.