广东工业大学学报 ›› 2021, Vol. 38 ›› Issue (01): 75-81.doi: 10.12052/gdutxb.200004

• 综合研究 • 上一篇    下一篇

具有Banach代数的锥度量空间中的公共不动点定理

洪育敏, 杨理平   

  1. 广东工业大学 应用数学学院，广东 广州 510520
  • 收稿日期:2020-01-03 出版日期:2021-01-25 发布日期:2020-12-21
  • 作者简介:洪育敏(1994-)，女，硕士研究生，主要研究方向为非线性泛函分析
  • 基金资助:
    国家自然科学基金资助项目(61374081)；教育部人文社科规划基金资助项目(14YJAZH095)；广东省自然科学基金资助项目(2015A030313485)；广州市科技计划项目(201707010494)

Common Fixed Point Theorems in Cone Metric Spaces over Banach Algebras

Hong Yu-min, Yang Li-ping   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-01-03 Online:2021-01-25 Published:2020-12-21

HTML

PDF (PC)

2696

摘要： 在去掉锥的正规性和映射的弱增性的条件下, 研究Banach代数锥度量空间中的公共不动点的存在性和唯一性, 其结果改进和推广了相关文献中的一些主要结论。

关键词: Banach代数, 锥度量空间, 公共不动点

Abstract: In this paper, we study the existence and uniqueness of common fixed points in cone metric spaces over Banach algebras without the normality of cone and the weakly increasing of mappings. The results improve and generalize some main conclusions in related literatures.

Key words: Banach Algebras, cone metric spaces, common fixed points

中图分类号: 

  • O177.91
[1] MICULESCU R, MIHAIL A. New fixed point theorems for set-valued contractions in b-metric spaces [J]. Journal of Fixed Point Theory and Applications, 2017, 19: 2153-2163.
[2] ALEKSIC S, HUANG H P, ZORAN D M, et al. Remarks on some fixed point results in b-metric spaces [J]. Journal of Fixed Point Theory and Applications, 2018, 20: 147.
[3] HUANG L G, ZHANG X. Cone metric spaces and fixed point theorems of contractive mappings [J]. Journal of Mathematical Analysis and Applications, 2007, 332: 1468-1476.
[4] LIU H, XU S. Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz map-pings [J]. Fixed Point Theory and Applications, 2013, 1: 1-10.
[5] RUDIN W. Functional Analysis[M]. 2nd ed. New York: McGeaw-Hill, 1991.
[6] XU S Y, RADENOVIC S. Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality [J]. Fixed Point Theory and Applications, 2014, 102: 1-12.
[7] HUANG H P, RADENOVIC S. Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications [J]. Journal of Nonlinear Sciences and Applications, 2015, 8: 787-799.
[8] MUJAHID A, JUNGCK G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces [J]. Journal of Mathematical Analysis and Applications, 2008, 341: 416-420.
[9] DIBARI C, VETRO P. ?-Pairs and common fixed points in cone metric spaces [J]. Rendiconti del Circolo Math-ematico di Palermo, 2008, 57: 279-285.
[10] KADELBURG Z, PAVLOVIC M, RADENOVIC S. Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces [J]. Computers Mathematics with Applications, 2010, 59: 3148-3159.
[11] ZORAN D M, RADENOVIC S, HUSSAIN N. A common fixed point theorem of Fisher in b-metric spaces [J]. Revista de la Real Academia de Ciencias Exactas Fisicasy Naturales Serie A-Matematicas, 2018, 113 (4): 949-956.
[12] HUANG H P, RADENOVIC S, DOSENOVIC T. Some common fixed point theorems on c-distance in cone metric spaces over Banach algebras [J]. Computers & Mathematics with Applications, 2015, 14: 180-193.
[13] 刘艳艳, 杨理平. 锥度量空间中c-距离的公共不动点定理[J]. 广东工业大学学报, 2019, 36(5): 43-47.
LIU Y Y, YANG L P. Common fixed point theorems for c-distances in cone metric spaces [J]. Journal of Guangdong University of Technology, 2019, 36(5): 43-47.
[14] 许涛, 贺飞, 刘俊楠. b-距离空间中含有四个映射的Ciri型公共不动点定理[J]. 应用泛函分析学报, 2017, 19(2): 165-175.
XU T, HE F, LIU J N. Ciri type common fixed point theorem with four mappings in b-distance space [J]. Acta Analysis Functionalis Applicata, 2017, 19(2): 165-175.
[15] SEDGHI S, SHOBKOLAEI N, SHAHRAKI M, et al. Common fixed point of four maps in S-metric spaces [J]. Mathematical Sciences, 2018, 12(2): 137-143.
[16] 韩艳, 许绍元. 半序锥度量空间中新公共不动点定理[J]. 应用数学, 2012, 25(1): 194-201.
HAN Y, XU S Y. A new common fixed point theorem in a space of semi-order taper quantities [J]. Mathematica Applicata, 2012, 25(1): 194-201.
[1] 刘艳艳, 杨理平. 锥度量空间中c-距离的公共不动点定理[J]. 广东工业大学学报, 2019, 36(05): 43-47.
[2] 陈盼, 孔伟铭, 杨理平. 锥度量空间中四个自映射的公共不动点定理[J]. 广东工业大学学报, 2014, 31(4): 79-84.
[3] 孔伟铭，杨理平. 锥度量空间中扩张映象对的公共不动点定理[J]. 广东工业大学学报, 2013, 30(1): 76-80.
[4] 杨理平； . 广义2-距离空间中映象列的公共不动点[J]. 广东工业大学学报, 2002, 19(4): 92-97.
[5] 杨理平； . 一类压缩型映象序列的公共不动点定理[J]. 广东工业大学学报, 1998, 15(4): 71-75.
[6] 杨理平； . 一类交换映象的公共不动点定理[J]. 广东工业大学学报, 1998, 15(2): 107-109.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发