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Generalized Lupas Operators
(Amer Inst Physics, 2018) Ilarslan, Hatice Gill Ince; Aral, Ali; Bascanbaz-Tunca, Gulen
In this work, by taking a continuously differentiable, increasing and unbounded function rho, we consider an extension of the Lupas operator L-n in the form L-n (f o rho(-1)) o rho for convenient functions f on [0, infinity). We give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.
On Multivariate Bleimann, Butzer and Hahn Operators
(SPRINGER BASEL AG, 2020) Soylemez, Dilek; Ari, Didem Aydin; Bascanbaz-Tunca, Gulen
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.