In this paper we deal with a sequence of positive linear operators ${{R_n}}^{[$eta$]}$</TEX> approximating functions on the unbounded interval [0, $infty$] which were firstly used by K. balazs and J. Szabados. We give pointwise estimates in the framework of polynomial weighted function spaces. Also we establish a Voronovskaja type theorem in the same weighted spaces for ${{K_n}}^{[$eta$]}$</TEX> operators, representing the integral generalization in Kantorovich sense of the ${{R_n}}^{[$eta$]}$</TEX>.