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Generalized Kantorovich forms of exponential sampling series

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Abstract

In this paper, we introduce a new family of operators by generalizing Kantorovich type of exponential sampling series by replacing integral means over exponentially spaced intervals with its more general analogue, Mellin Gauss Weierstrass singular integrals. Pointwise convergence of the family of operators is presented and a quantitative form of the convergence using a logarithmic modulus of continuity is given. Moreover, considering locally regular functions, an asymptotic formula in the sense of Voronovskaja is obtained. By introducing a new modulus of continuity for functions belonging to logarithmic weighted space of functions, a rate of convergence is obtained. Some examples of kernels satisfying the obtained results are presented.

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Authors and Affiliations

  1. Faculty of Science and Arts, Department of Mathematics, Kirikkale University, Yahsihan, 71450, Kirikkale, Turkey

    Ali Aral

  2. Faculty of Science, Department of Mathematics, Selcuk University, Selcuklu, 42003, Konya, Turkey

    Tuncer Acar & Sadettin Kursun

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  1. Ali Aral
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  2. Tuncer Acar
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  3. Sadettin Kursun
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Aral, A., Acar, T. & Kursun, S. Generalized Kantorovich forms of exponential sampling series. Anal.Math.Phys. 12, 50 (2022). https://doi.org/10.1007/s13324-022-00667-9

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  • DOI: https://doi.org/10.1007/s13324-022-00667-9

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