Characterization of Deferred Statistical Convergence of Order α 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,∞ ) , via deferred statistical convergence of order α , (0<α ≤ 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.