Pointwise convergence of generalized Kantorovich exponential sampling series
Title | Pointwise convergence of generalized Kantorovich exponential sampling series |
Publication Type | Journal Article |
Year of Publication | 2023 |
Authors | Acar, T, Kursun, S |
Journal | Dolomites Research Notes on Approximation |
Volume | 16 |
Issue | 1 |
Pagination | 1-10 |
Date Published | 01/2023 |
Publisher | Padova University Press |
Place Published | Padova, IT |
ISSN Number | 2035-6803 |
Abstract | 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. |
URL | https://drna.padovauniversitypress.it/2023/2/1 |
DOI | 10.14658/pupj-drna-2023-2-1 |