Yildiz, Sevda2025-03-232025-03-2320212651-477Xhttps://doi.org/10.15672/hujms.796762https://search.trdizin.gov.tr/tr/yayin/detay/493999https://hdl.handle.net/11486/5009In this paper, we first introduce the notions of F-relative modular convergence and F-relative strong convergence for double sequences of functions. Then we prove some Korovkin-type approximation theorems via F-relative A-summation process on modular spaces for double sequences of positive linear operators. Also, we present a non-trivial application such that our Korovkin-type approximation results in modular spaces are stronger than the classical ones and we present some estimates of rates of convergence for abstract Korovkin-type theorems. Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.eninfo:eu-repo/semantics/openAccessmodular spacesdouble sequencematrix summabilityfilter convergenceabstract Korovkin theoremArticle5041047106210.15672/hujms.7967622-s2.0-85113204423Q2493999WOS:000687954300012Q2