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Miskolc Mathematical Notes
Article . 2004 . Peer-reviewed
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Kantorovich-Schurer bivariate operators

Authors: Bărbosu, Dan;

Kantorovich-Schurer bivariate operators

Abstract

Summary: Let \(p,q\) be two non-negative given integers. The sequence \((\tilde{K}_{m,n,p,q})_{m,n\in N}\), \(\tilde{K}_{m,n,p,q}:L_1([0,1]\times [0,1])\to C([0,1]\times[0,1])\), \[ \left(\tilde{K}_{m,n,p,q} f\right)(x,y) \] \[ = (m+p+1)(n+p+1)\times \sum\nolimits^{m+p}_{k=0}\sum\nolimits^{n+q}_{j=0} \tilde{p}_{m,k}(x)\tilde{p}_{n j}(y)\int\nolimits^{\frac{k+1}{m+p+1}}_{\frac{k}{m+p+1}} \int^{\frac{j+1}{n+q+1}}_{\frac{j}{n+q+1}}f(s,t) ds\,dt \] of bivariate Kantorovich-Schurer operators is constructed and some approximation properties of the sequence \(\left\{\tilde{K}_{m,n,p,q} f\right\}_{m,n\in N}\) are studied.

Country
Hungary
Keywords

Sisha-Mond theorem, Bernstein operator, QA Mathematics / matematika, Schurer operator, first order modulus of smoothness, bivariate operator, Approximation by positive operators, Multidimensional problems, linear positive operator, Kantorovich operator, Korovkin theorem

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
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