Szász–Mirakjan–Kantorovich operator

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

${\displaystyle [{\mathcal {T}}_{n}(f)](x)=ne^{-nx}\sum _{k=0}^{\infty }{{\frac {(nx)^{k}}{k!}}\int _{k/n}^{(k+1)/n}f(t)\,dt}}$

where ${\displaystyle x\in [0,\infty )\subset \mathbb {R} }$ and ${\displaystyle n\in \mathbb {N} }$.[1]

See also

• Szász–Mirakyan operator

Notes

1. Walczak, Zbigniew (2002). "On approximation by modified Szasz–Mirakyan operators". Glasnik Matematički. 37 (57): 303–319.

References

• Totik, V. (June 1983). "Approximation by Szász–Mirakjan–-Kantorovich operators in L^p (p > 1)". Analysis Mathematica (in Russian). 9 (2): 147–167. doi:10.1007/BF01982010. MR 0720083. Zbl 0513.41012.