The present paper is a continuation of the recent paper "A. Aral, T. Acar, S. Kursun, Generalized Kantorovich forms of exponential sampling series, Anal. Math. Pyh., 12:50, 1-19 (2022)" in which a new Kantorovich form of generalized exponential sampling series K χ,G w has been introduced by means of Mellin Gauss Weierstrass singular integrals. In this paper, in order to investigate pointwise convergence of the family of operators K χ,G w , we first obtain an estimate for the remainder of Mellin-Taylor’s formula and by this estimate we give the Voronovskaya theorem in quantitative form by means of Mellin derivatives. Furthermore, we present quantitative Voronovskaya theorem for difference of family of operators K χ,G w and generalized exponential sampling series E χ w . The results are examined by illustrative numerical examples.
Pointwise convergence of generalized Kantorovich exponential sampling series
Acar T., Kursun S. (2023) "Pointwise convergence of generalized Kantorovich exponential sampling series " Dolomites Research Notes on Approximation, 16(2), 1-10. DOI: 10.14658/PUPJ-DRNA-2023-2-1
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Dolomites Research Notes on Approximation
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