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Bivariate generalized Kantorovich-type exponential sampling series

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Abstract

In this paper, we introduce a family generalized Kantorovich-type exponential sampling operators of bivariate functions by using the bivariate Mellin-Gauss-Weierstrass operator. Approximation behaviour of the series is established at continuity points of log-uniformly continuous functions. A rate of convergence of the family of operators is presented by means of logarithmic modulus of continuity and a Voronovskaja-type theorem is proved in order to determine rate of pointwise convergence. Convergence of the family of operators is also investigated for functions belonging to weighted space. Furthermore, some examples of the kernels which support our results are given.

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... Concurrently, significant progress has been made in the study of approximation results by means of exponential-type operators (see, e.g., [1][2][3][4][5][6][7]12]). In this respect, Bardaro, Faina, and Mantellini [9] introduced a new family of sampling-type operators, known as exponential sampling series. ...
... Let x ∈ R + be fixed. The approximation error |(K χ w f )(x) − f (x)| can be decomposed by I 1 + I 2 , as illustrated in the preliminary steps of the proof of Theorem 6 (see (1)). Now, we focus on estimating I 1 . ...
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... For other publications on the exponential sampling series and its different forms (see, [12][13][14][15][40][41][42]). Moreover, for the approximation properties of generalized exponential sampling series and its different forms in logarithmic weighted spaces of continuous functions (see also [5][6][7]). ...
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... These advances have enabled the study of phenomena like light scattering and diffraction. As research continues, new applications and modifications are emerging, as seen in works covering weighted approximations by samplingtype operators (see, e.g., [1,4,5,7,29,30,37]). ...
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... Numerous results have been published on the exponential sampling series and Kantorovich forms; see, for example, [32][33][34][35][36][37][38][39][40][41][42]. For other publishes on approximation theory and sampling type series, we refer the readers to [43,44]. ...
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