The max-product generalized sampling operators: convergence and quantitative estimates

Lucian Coroianu, Danilo Costarelli, Sorin G. Gal and Gianluca Vinti

Applied Mathematics and Computation, 2019, vol. 355, issue C, 173-183

Abstract: In this paper we study the max-product version of the generalized sampling operators based upon a general kernel function. In particular, we prove pointwise and uniform convergence for the above operators, together with a certain quantitative Jackson-type estimate based on the first order modulus of continuity of the function being approximated. The proof of the proposed results are based on the definition of the so-called generalized absolute moments. By the proposed approach, the achieved approximation results can be applied for several type of kernels, not necessarily duration-limited, such as the sinc-function, the Fejér kernel and many others. Examples of kernels with compact support for which the above theory holds can be given, for example, by the well-known central B-splines.

Keywords: Quantitative Jackson-type estimate; Max-product generalized sampling operators; Modulus of continuity; Convergence; Kernel (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:355:y:2019:i:c:p:173-183

DOI: 10.1016/j.amc.2019.02.076

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