View source for Szász–Mirakjan–Kantorovich operator

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

:<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''</sup> (''p''&nbsp;>&nbsp;1)|journal=Analysis Mathematica|volume=9|issue=2|pages=147–167|doi=10.1007/BF01982010|mr=720083| zbl = 0513.41012|language=ru}}

{{DEFAULTSORT:Szasz-Mirakjan-Kantorovich Operator}}
[[Category:Approximation theory]]


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