Ayhan, Burcu Sunbul2025-02-202025-02-2020250037-87122175-1188https://doi.org/10.5269/bspm.68959https://hdl.handle.net/20.500.12846/1556The main purpose of this study is to introduce and study two new classes of continuity called eR- continuous functions and weakly eR-continuous functions via e-regular sets. Both forms of continuous functions we have described are stronger than the weakly e-continuity. Furthermore, we obtain various characterizations of weakly eR-continuous functions. In addition, we examine not only the relations of these functions with some other forms of existing continuous functions, but also some of their fundamental properties.eninfo:eu-repo/semantics/closedAccesse-regular sete-connectednesseR-continuityweakly eR-continuityArticle4310.5269/bspm.68959Q2WOS:001416008000032