In functional analysis, a discipline within mathematics, the Szász–Mirakjan–Kantorovich operators are defined by
[ T n ( f ) ] ( x ) = n e − n x ∑ k = 0 ∞ ( n x ) k k ! ∫ k / n ( k + 1 ) / n f ( t ) d t {\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 x ∈ [ 0 , ∞ ) ⊂ R {\displaystyle x\in [0,\infty )\subset \mathbb {R} } and n ∈ N {\displaystyle n\in \mathbb {N} } .
See also Szász–Mirakyan operator
Notes
References Totik, V. (June 1983). "Approximation by Szász–Mirakjan–-Kantorovich operators in Lp (p > 1)". Analysis Mathematica (in Russian). 9 (2): 147–167. doi:10.1007/BF01982010. MR 0720083. S2CID 123797519. Zbl 0513.41012.