Modified Sz´asz-Mirakjan operators of integral form


Radu Păltănea


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carpathian_2008_24_3_378_385

We deal with approximation by a modified family of Szasz-Mirakjan operators, with parameters ´ ρ > 0, α > 0, which reproduce linear functions: L ρ α(f, x) = e −αx f(0) + X∞ k=1 (αx) k k! Z ∞ 0 αρkρ Γ(kρ) · e −αρt(αt) kρ−1 f(t) dt , where x ≥ 0 and f : [0, ∞) → R is taken such that this formula is well defined.