Characterization of Absolute and Uniform Continuity

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:5
Characterization of Absolute and Uniform Continuity

Characterization of Absolute and Uniform Continuity

Authors : İsmail ASLAN, Oktay DUMAN

Pages : 1550-1565

Doi:10.15672/hujms.585581

View : 21 | Download : 7

Publication Date : 2020-10-06

Article Type : Research Paper

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

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