The study titled “Some Korovkin type approximation applications of power series methods” was published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas volume by ITU Mathematics Engineering faculty member Res. Assis. Havva Uluçay.
Function theoretical type summability methods have various applications. One of these applications is making a Korovkin type approximation with a sequence of positive linear operators whenever the ordinary convergence of the space fails. In this paper, it is proved some Korovkin type approximation theorems in Lq [a, b], the space of all measurable real valued qth power Lebesgue integrable functions defined on [a, b] for q ≥ 1, and C[a, b], the space of all continuous real valued functions defined on [a,b], via statistical convergence with respect to power series (summability) methods, integral summability methods and μ-statistical convergence of the power series transforms of positive linear operators. It is also shown with examples that the results obtained in the present paper are stronger than some existing approximation theorems in the literature.