Dolomites Research Notes on Approximation

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.