满足弱压缩条件及性质的4个映射公共不动点定理

2016-10-13 23:27常慧杰桑彦彬
高师理科学刊 2016年1期
关键词:不动点重合度量

常慧杰,桑彦彬



满足弱压缩条件及性质的4个映射公共不动点定理

常慧杰[1],桑彦彬

(中北大学 理学院,山西 太原 030051)

利用偶尔弱相容自映射与性质,建立了一类4个映射公共不动点的存在性定理,其中4个映射皆满足弱压缩条件.

4映射;公共不动点;偶尔弱相容

1引言及预备知识

定义1[3]设和是度量空间中的自映射.如果对于中的某个成立,则称为和的一个重合点,和在中重合点的集合记为,称为和的重合像点.

定义2[4]如果在中存在一个序列,使得对于中的某个成立,则称满足性质.

定义3[5]如果存在,使得成立,则称为偶尔弱相容.

定义4[6]令是一个度量空间,,,,为中的4个自映射.若在中存在序列和,使得对于中的某个成立,则称和满足公共性质.

引理[7]令,则,且时,.

2主要结果及证明

考虑

对式(12)两端取极限,由式(10)和式(11)可知,.所以,因此.

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Common fixed point theorems for four mappings satisfyingweakly contractive conditions and property

CHANG Hui-jie,SANG Yan-bin

(School of Science,North University of China,Taiyuan 030051,China)

By using of occasionally weakly compatible selfmaps and property,established the existence results of common fixed points for four mappings satisfyingweakly contractive conditions.

four mappings;common fixed points;occasionally weakly compatible

O157.5

A doi:10.3969/j.issn.1007-9831.2016.01.006

2015-10-14

中北大学校基金项目

常慧杰(1989-),男,山西太原人,在读硕士研究生,从事非线性泛函研究.E-mail:852740174@qq.com

桑彦彬(1979-),男,山西泽州人,副教授,博士,从事非线性泛函分析研究.E-mail:sangyanbin@126.com

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