Year: 2026
Type: article
Abstract: In this paper, we begin by establishing a rigorous upper bound for the difference between the operators and , providing a precise measure of the approximation error inherent in the proposed operators. Building on this foundation, we proceed to derive a quantitative Voronovskaja-type formula, which offers a detailed characterization of the asymptotic behavior of the operator under consideration. Finally, to demonstrate the practical relevance and applicability of the theoretical results, we present several illustrative examples of kernels that are compatible with the proposed framework. In this paper, we begin by establishing a rigorous upper bound for the difference between the operators and , providing a precise measure of the approximation error inherent in the proposed operators. Building on this foundation, we proceed to derive a quantitative Voronovskaja-type formula, which offers a detailed characterization of the asymptotic behavior of the operator under consideration. Finally, to demonstrate the practical relevance and applicability of the theoretical results, we present several illustrative examples of kernels that are compatible with the proposed framework.
Author: Sadettin Kursun
Institutions: Milli Savunma Üniversitesi, Turkish Military Academy
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7154042124