Periodic Korovkin Theorem via $P_{p}^{2}$-Statistical $\mathcal{A}$-Summation Process

Abstract

In the current research, we investigate and establish Korovkin-type approximation theorems for linear operators defined on the space of all $% 2\pi $-periodic and real valued continuous functions on $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2}$ by means of $\mathcal{A}$-summation process via statistical convergence with respect to power series method. We demonstrate with an example how our theory is more strong than previously studied. Additionally, we research the rate of convergence of positive linear operators defined on this space.

Keywords

• korovkin theorem
• periodic functions
• power series method
• rates of convergence
• statistical convergence