Szász–Mirakjan–Kantorovich operator

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

[math]\displaystyle{ [\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]\displaystyle{ x\in[0,\infty)\subset\mathbb{R} }[/math] and [math]\displaystyle{ n\in\mathbb{N} }[/math].

See also

• Szász–Mirakyan operator

References

• Totik, V. (June 1983). "Approximation by Szász–Mirakjan–-Kantorovich operators in L^p (p > 1)" (in ru). Analysis Mathematica 9 (2): 147–167. doi:10.1007/BF01982010.