Korovkin-type Approximation Theorems for Functions with the Help of ℐ-statistical Convergence

The basic aim of this work is to prove the approximation problem for a sequence of positive linear operators (PLOs) acting from HωD to CbD where D=0,∞ by means of the notion of ℐ-statistical uniform convergence. Next, an example will be given where our new approximation theorem works but some of the previous results do not. Also, the rate of ℐ-statistical uniform convergence for the sequences of PLOs is computed by way of the modulus of smoothness. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.