The concept of f-statistical convergence which is, in fact, a generalization of statistical convergence, has been introduced recently by Aizpuru et al. (Quaest. Math. 37: 525–530, 2014). The main object of this paper is to prove an f-statistical analog of the classical Korovkin type approximation theorem of Boyanov and Veselinov. It is shown that the f-statistical analog is intermediate between the classical theorem and its statistical analog. As an application, we estimate the rate of f-statistical convergence of the sequence of positive linear operators defined from C^*[0,∞) into itself.

Keywords: modulus function, statistical convergence, positive linear operator, rate of convergence, Korovkin type approximation theorem.