On Approximation by Kantorovich Exponential Sampling Operators

Abstract

In this article, we extend our study of Kantorovich type exponential sampling operators introduced in [34]. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these operators. Subsequently, we prove the estimates concerning the order of convergence for these linear combinations. Finally, we give some examples of kernels along with the graphical representations.

Semi‐discrete operators in multivariate setting: Convergence properties and applications

“…They are called (univariate) “exponential sampling series.” The generalized version of such series was introduced in Bardaro et al [11]. Later on Kantorovich [12] versions were studied in previous studies [13–15] while a Durrmeyer version was introduced in Bardaro and Mantellini [16] (see also Bajpeyi et al [17]). In Bardaro et al [18], a two‐dimensional version was studied with the aim to obtain mathematical models for the study of the propagation of seismic waves (a general multivariate version was recently studied in Kursun et al [19]).…”

On bivariate Kantorovich exponential sampling series

“…Further, the generalized form of Kantorovich exponential sampling series was studied in Aral et al [17]. The approximation of discontinuous signals by the Kantorovich exponential sampling series was discussed in Kumar et al [18], and its inverse approximation results are given in Bajpeyi et al [19]. The Kantorovich type modification of sampling operators has been a topic of deep interest due to its wide applications in approximation theory.…”

“…This provides an useful tool to approximate not necessarily continuous but Lebesgue integrable functions by using its sample values at the nodes $$$ {\left({e}^{k/w}\right)}_{w>0},k\in \mathrm{\mathbb{Z}} $$$. To improve the order of approximation for the above family, the linear combination of these operators was considered in Bajpeyi and Kumar [16]. Further, the generalized form of Kantorovich exponential sampling series was studied in Aral et al [17].…”