- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 5
- Characterization of Absolute and Uniform Continuity
Characterization of Absolute and Uniform Continuity
Authors : Ismail Aslan, Oktay Duman
Pages : 1550-1565
Doi:10.15672/hujms.585581
View : 12 | Download : 5
Publication Date : 2020-10-06
Article Type : Research
Abstract :In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants. We observe that Bell-type summability methods are quite effective to generalize and improve some related results in the literature. At the end of the paper, we discuss some special cases and applications.Keywords : Summability process, absolute continuity, uniform continuity, nonlinear integral operators, bounded variation