Characterization of Absolute and Uniform Continuity

Year 2020, , 1550 - 1565, 06.10.2020

İsmail Aslan , Oktay Duman

https://doi.org/10.15672/hujms.585581

Cited By: 5

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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