Dirik, FadimeDemirci, KamilYıldız, Sevda2026-04-252026-04-252026978-303193278-62194-1009https://doi.org/10.1007/978-3-031-93279-3_5https://hdl.handle.net/11486/79938th International conference Approximation Theory and Special Functions, ATSF 2024 -- 4 September 2024 through 7 September 2024 -- Ankara -- 347299The 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.eninfo:eu-repo/semantics/closedAccessIdeal convergenceKorovkin theoremStatistical convergenceThe Bleimann, Butzer and Hahn operatorsℐ-statistical convergenceConference Object503 PROMS11312210.1007/978-3-031-93279-3_52-s2.0-105029616934Q4