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

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

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.

Suggested Citation

  • Coroianu, Lucian & Costarelli, Danilo & Gal, Sorin G. & Vinti, Gianluca, 2019. "The max-product generalized sampling operators: convergence and quantitative estimates," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 173-183.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:173-183
    DOI: 10.1016/j.amc.2019.02.076
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    References listed on IDEAS

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    1. Xing, Yan & Xu, Ren-zheng & Tan, Jie-qing & Fan, Wen & Hong, Ling, 2015. "A class of generalized B-spline quaternion curves," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 288-300.
    2. Mehdi Rezaeian Zadeh & Seifollah Amin & Davar Khalili & Vijay Singh, 2010. "Daily Outflow Prediction by Multi Layer Perceptron with Logistic Sigmoid and Tangent Sigmoid Activation Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(11), pages 2673-2688, September.
    3. Asdrubali, Francesco & Baldinelli, Giorgio & Bianchi, Francesco & Costarelli, Danilo & Rotili, Antonella & Seracini, Marco & Vinti, Gianluca, 2018. "Detection of thermal bridges from thermographic images by means of image processing approximation algorithms," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 160-171.
    4. Danilo Costarelli & Gianluca Vinti, 2017. "Convergence for a family of neural network operators in Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(2-3), pages 226-235, February.
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    Cited by:

    1. Gökçer, Türkan Yeliz & Aslan, İsmail, 2022. "Approximation by Kantorovich-type max-min operators and its applications," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    2. Kadak, Ugur, 2022. "Max-product type multivariate sampling operators and applications to image processing," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Costarelli, Danilo & Seracini, Marco & Vinti, Gianluca, 2020. "A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods," Applied Mathematics and Computation, Elsevier, vol. 374(C).

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