Generalized Kantorovich forms of exponential sampling series
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Basel Ag
Access Rights
info:eu-repo/semantics/closedAccess
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.
Description
Keywords
Exponential sampling series; Kantorovich operators; Gauss-Weierstrass kernel; Mellin differential operator; Pointwise convergence; Asymptotic formula
Journal or Series
Analysis and Mathematical Physics
WoS Q Value
Q1
Scopus Q Value
Q1
Volume
12
Issue
2
