Fractional Korovkin-type Results by P-statistical Convergence

Abstract

The author obtains fractional Korovkin-type results by statistical convergence which is based on a power series. In approximation theory, Korovkin-type theorems are used frequently since they give the opportunity to determine the uniform convergence of positive linear operators to identity operators by minimum calculations. These theorems are investigated by using different concepts of convergences, changing the function spaces and test functions. These results are also examined by quantum calculus and fractional calculus. In the existing literature there are some results obtained by fractional calculus but rarely. Therefore, the author’s aim is to obtain fractional Korovkin-type results and illustrate examples that make important contributions to existing literature since statistical convergence and P-statistical convergence do not imply each other. © 2025 Ferit Gürbüz.