Gazi University Journal of Science 2147-1762 Gazi University 10.35378/gujs.1775191 Approximation Theory and Asymptotic Methods Yaklaşım Teorisi ve Asimptotik Yöntemler Bivariate Generalized Kantorovich Forms of Exponential Sampling Series: Some New Results https://orcid.org/0000-0001-6697-9627 Kursun Sadettin NATIONAL DEFENSE UNIVERSITY, TURKISH MILITARY ACADEMY Advanced Online Publication 09 01 2025 02 25 2026 Copyright © 1988, Gazi University Journal of Science 1988 Gazi University Journal of Science

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.

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