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In [[functional analysis]], a discipline within [[mathematics]], the '''Szász–Mirakjan–Kantorovich operators''' are defined by


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:<math>[\mathcal{T}_n(f)](x)=ne^{-nx}\sum_{k=0}^\infty{\frac{(nx)^k}{k!}\int_{k/n}^{(k+1)/n}f(t)\,dt}</math>
 
where <math>x\in[0,\infty)\subset\mathbb{R}</math> and <math>n\in\mathbb{N}</math>.<ref name="Walczak">{{cite journal|last=Walczak|first=Zbigniew|year=2002|title=On approximation by modified Szasz–Mirakyan operators|journal=Glasnik Matematički|volume=37|issue=57|pages=303–319|url=http://web.math.hr/glasnik/vol_37/no2_08.html}}</ref>
 
==See also==
*[[Szász–Mirakyan operator]]
 
==Notes==
<references/>
 
==References==
*{{cite journal|last=Totik|first=V.|authorlink=Vilmos Totik|date=June 1983|title=Approximation by Szász–Mirakjan–-Kantorovich operators in ''L''<sup>''p''</sub> (''p''&nbsp;>&nbsp;1)|journal=Analysis Mathematica|volume=9|issue=2|pages=147–167|doi=10.1007/BF01982010|mr=85h:41053 | zbl = 0513.41012}} {{ru icon}}
 
{{DEFAULTSORT:Szasz-Mirakjan-Kantorovich Operator}}
[[Category:Approximation theory]]
 
 
{{mathanalysis-stub}}

Revision as of 05:58, 18 February 2013

In functional analysis, a discipline within mathematics, the Szász–Mirakjan–Kantorovich operators are defined by

where and .[1]

See also

Notes

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References

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