An approximation process of Kantorovich type (Q2770609)

A Kantorovich-type modification of the well known operators NEWLINE\[NEWLINE (R_nf)=\frac{1}{(1+a_n x)^n} \sum_{k=0}^n\binom{n}{k}(a_nx)^kf(\frac{k}{b_n}), \quad x\geq 0,\;n\in \mathbb{N} NEWLINE\]NEWLINE is introduced. In particular, the author changes \(f(\frac{k}{b_n})\) by the integral mean NEWLINE\[NEWLINEna_n\int_{k/(na_n)}^{(k+1)/(na_n)}f(t) dt.NEWLINE\]NEWLINE The author computes the degree of approximation associated to these operators in certain function spaces. Concretely, he obtains estimations for local \(\text{Lip}_{\alpha}\) functions. The most interesting result of the paper, for this reviewer, is Theorem 4, where some estimations are obtained for functions with jump discontinuities.