Characterization of absolute and uniform continuity

被引：10

作者：

Aslan, Ismail ^{[1
]}

Duman, Oktay ^{[2
]}

机构：

[1] Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey

[2] TOBB Univ Econ & Technol, Dept Math, TR-06530 Ankara, Turkey

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2020年 / 49卷 / 05期

关键词：

summability process; absolute continuity; uniform continuity; nonlinear integral operators; bounded variation; CONVERGENCE; SUMMABILITY;

D O I：

10.15672/hujms.585581

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1550 / 1565

页数：16

共 33 条

[1]

Anastassiou GA, 2011, INTEL SYST REF LIBR, V14, P1, DOI 10.1007/978-3-642-19826-7

[2]

Angeloni L., 2014, NEW PERSPECTIVES APP, P299

[3] Convergence in Variation and Rate of Approximation for Nonlinear Integral Operators of Convolution Type [J].