title: New type continuities via Abel convergence.
abstract: We investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is a closed subset of continuous functions.
authors.affiliation: Department of Mathematics, Maltepe University, Marmara Eğıtım Köyü, Maltepe, 34857 İstanbul, Turkey.
authors.forename: Huseyin
authors.identifier: 0000-0001-7344-5826
authors.initials: H
authors.lastname: Cakalli
authors.affiliation: Department of Mathematics, Sakarya University, Sakarya, 54050 İstanbul, Turkey.
authors.forename: Mehmet
authors.initials: M
authors.lastname: Albayrak
mesh_terms: D008433:Mathematics / Q000379:methods; D008962:Models, Theoretical