Fractional Trigonometric Korovkin Theory via Statistical Convergence with Respect to Power Series Method

Abstract

In approximation theory, Korovkin-type theorems are well used since they provide us to determine the uniform convergence of positive linear operators to identity by using only three functions {1, x, x²}. They have been investigated in different function spaces, generally, by using different concepts of convergences, by using -calculus and rarely fractional calculus. In this chapter, by fractional calculus which is a branch of analysis dealing with derivatives and integrals of arbitrary order, fractional Korovkin-type trigonometric approximation results will be presented via -statistical convergence which depends on a power series method. Also, as an application of our theorems various type examples will be constructed.