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On Multivariate Bleimann, Butzer and Hahn Operators

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Abstract

In this paper, we state a Korovkin-type theorem for uniform approximation of functions, belonging to a class generated by multivariable function of modulus of continuity, by the sequence of multivariate positive linear operators. Then, using this theorem, we investigate the corresponding uniform approximation result for the multivariate Bleimann, Butzer and Hahn operators which are not in a tensor product design. Moreover, we give an elementary proof that these operators are non-increasing in n when the attached function is convex and non-increasing and we add a graphical example.

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Acknowledgements

The authors are grateful to the anonymous reviewer for valuable suggestions which greatly improved this paper.

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Authors and Affiliations

  1. Department of Mathematics, Selçuk University, Faculty of Science, 42003, Selçuklu, Konya, Turkey

    Dilek Söylemez

  2. Department of Mathematics, Kırıkkale University, Faculty of Arts and Science, Yahşihan, Kırıkkale, Turkey

    Didem Aydın Arı

  3. Department of Mathematics, Ankara University, Faculty of Science, Beşevler, 06100, Ankara, Turkey

    Gülen Başcanbaz-Tunca

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  1. Dilek Söylemez
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  2. Didem Aydın Arı
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  3. Gülen Başcanbaz-Tunca
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Correspondence to Gülen Başcanbaz-Tunca.

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Söylemez, D., Arı, D.A. & Başcanbaz-Tunca, G. On Multivariate Bleimann, Butzer and Hahn Operators. Mediterr. J. Math. 17, 191 (2020). https://doi.org/10.1007/s00009-020-01633-0

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  • DOI: https://doi.org/10.1007/s00009-020-01633-0

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