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Approximation by Kantorovich-type max-min operators and its applications

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  • Gökçer, Türkan Yeliz
  • Aslan, İsmail

Abstract

In this study, we construct Kantorovich variant of max-min kind operators, which are nonlinear. By using these new operators, we obtain some uniform approximation results in N-dimension (N≥1). Then, we estimate the error with the help of Hölder continuous functions and modulus of continuity. Furthermore, we give some illustrative applications to verify our theory and also investigate some shape-preserving properties of Kantorovich-type max-min Bernstein operator. Lastly, we examine the image processing implementation of our results via Kantorovich-type max-min Shepard operator.

Suggested Citation

  • Gökçer, Türkan Yeliz & Aslan, İsmail, 2022. "Approximation by Kantorovich-type max-min operators and its applications," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322000972
    DOI: 10.1016/j.amc.2022.127011
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    References listed on IDEAS

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    1. Barnabás Bede & Lucian Coroianu & Sorin G. Gal, 2009. "Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-26, December.
    2. 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.
    3. Ismail Aslan & Oktay Duman, 2020. "Approximation by nonlinear integral operators via summability process," Mathematische Nachrichten, Wiley Blackwell, vol. 293(3), pages 430-448, March.
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    Cited by:

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