Characterization of Deferred Statistical Convergence of Order \(\alpha \) for Positive Linear Operators and Application to Generalized Bernstein Polynomials

In the present paper, we establish the Korovkin type theorems concerning positive linear operators defined for functions on [a, b] and also for functions on \([0,\infty )\) $[0,\infty )$ , via deferred statistical convergence of order \(\alpha\) $\alpha$ , \((0<\alpha \le 1)\) $(0<\alpha \le 1)$ . Further, we illustrate the application of our study to the generalized Bernstein polynomials introduced by Cao (J Math Anal Appl 209:140–146, 1997) and furnish an example to show that our Theorem 3 is a non-trivial generalization of the classical Korovkin type theorem.