New Type Continuities via Abel Convergence

被引：15

作者：

Cakalli, Huseyin ^{[1
]}

Albayrak, Mehmet ^{[2
]}

机构：

[1] Maltepe Univ, Dept Math, TR-34857 Istanbul, Turkey

[2] Sakarya Univ, Dept Math, TR-54050 Istanbul, Turkey

来源：

SCIENTIFIC WORLD JOURNAL | 2014年

关键词：

STATISTICAL CONVERGENCE; SEQUENTIAL DEFINITIONS; SUMMABILITY;

D O I：

10.1155/2014/398379

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：6

共 27 条

[1]

Abel N. H., 1826, Journal fur Math., V1, P311, DOI 10.1515/crll.1826.1.311

[2]

[Anonymous], 2002, Publ. Inst. Math. (Belgr.)

[3] Some best possible Tauberian results for Abel and Cesaro summability [J].