关于序γαβ-理想统计收敛的模糊数列空间  

On sequence spaces of fuzzy numbers forαβideal statistical convergence of orderγ

作　　者：冯雪 FENG Xue(College of Mathematics and Statics,Qinghai Minzu University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007

出　　处：《哈尔滨商业大学学报（自然科学版）》2022年第4期469-476,512,共9页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(11761056,11665019)青海省自然科学基金(2020-ZJ-920)。

摘　　要：以非降正数列a(n)、β(n)为框架,将模糊数列统计收敛和强收敛置于理想意义下,定义了两种新的模糊数列收敛的概念—关于序γαβ-理想统计收敛和关于序γ强αβ-理想收敛.同时,证明了这两种收敛的模糊数列空间的性质,以及这两种收敛之间的相互关系.给定模糊数列x={x_(k)},若它是强αβ-收敛的模糊数列,则x={x_(k)}一定是αβ-理想统计收敛的;当模糊数列x={x_(k)}有界时,反之成立.In the framework of non decreasing positive sequence,two new concepts of fuzzy sequence convergence have been defined in the ideal sense of statistical convergence and strong convergence of fuzzy sequence——theαβ-ideal statistical convergence and stronglyαβ-ideal convergence of orderγfor a sequence of fuzzy numbers.At the same time,the properties of two convergent fuzzy sequence spaces and the relationship between these two kinds of convergence have been proved.Given a fuzzy sequence x={x_(k)},if it was a stronglyαβ-convergent fuzzy sequence,it must beαβ-ideal statistical convergence;when x={x_(k)} was bounded,the contrary was true.

关 键 词：模糊数 模糊数列 理想统计收敛 强理想收敛 模糊数列空间 序 

分 类 号：O159[理学—数学]