Bivariate Generalized Kantorovich Forms of Exponential Sampling Series: Some New Results

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.  

Keywords

• Exponential-type sampling operators
• An upper bound
• A quantitative form of Voronovskaja-type theorem
• Examples of kernels

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