自然科学版
陕西师范大学学报(自然科学版)
数学与计算机科学
基于Orlicz函数及强缺项收敛的模糊数列空间
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巩增泰, 冯雪
(西北师范大学 数学与统计学院, 甘肃 兰州 730070)
巩增泰,男,教授,博士生导师,研究方向为模糊分析学。E-mail:gongzt@nwnu.edu.cn
摘要:
作为缺项统计收敛模糊数列空间的推广,基于Orlicz函数,在定义模糊数列强缺项收敛的基础上,提出和讨论了三类基于Orlicz函数的模糊数列空间F(M,θ,p),F0(M,θ,p)和F∞(M,θ,p),并证明了空间的线性性质;最后通过研究模糊数列强缺项收敛与缺项统计收敛之间、强缺项收敛与强收敛之间的相互关系,得到几类基于Orlicz函数的模糊数列空间的包含关系。
关键词:
模糊数; Orlicz函数; 模糊数列空间
收稿日期:
2014-05-28
中图分类号:
O159
文献标识码:
A
文章编号:
1672-4291(2015)01-0001-07doi:10.15983/j.cnki.jsnu.2015.01.111
基金项目:
国家自然科学基金资助项目(11461062,61262022); 甘肃省自然科学基金资助项目(1208RJZA251)
Doi:
On sequence spaces of fuzzy numbers based on Orlicz functions and strongly lacunary convergence
GONG Zengtai, FENG Xue
(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China)
Abstract:
As an extension of the lacunary statistical convergent sequence space of fuzzy numbers,some sequence spaces of fuzzy numbers,F(M,θ,p),F0(M,θ,p) and F∞(M,θ,p) based on Orlicz functions and strongly lacunary convergence are defined and discussed.It is shown that the spaces are linear spaces.In addition,the relationships of them are investigated by means of the discussion of strongly lacunary convergence,lacunary statistical convergence and strong convergence for the sequence of fuzzy numbers.
KeyWords:
fuzzy numbers; Orlicz functions; sequence spaces of fuzzy numbers