TVS -值锥度量空间上四个映射的唯一公共不动点

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 172-181.

TVS -值锥度量空间上四个映射的唯一公共不动点

朴勇杰, 金海兰, 金元峰

延边大学理学院数学系吉林延吉 133002

收稿日期:2013-10-08 修回日期:2014-11-06 出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金(11361064,11261062)和吉林省教育厅科研项目(吉教科合字2011[434])

Unique Common Fixed Points for Four Mappings on |TVS-Valued Cone Metric Spaces

PIAO Yong-Jie, JIN Hai-Lan, JIN Yuan-Feng

Department of Mathematics, College of Science, |Yanbian University, Jinlin |Yanji |133002

Received:2013-10-08 Revised:2014-11-06 Online:2015-02-25 Published:2015-02-25

摘要/Abstract

摘要：

在非完备的拓扑线性空间值锥度量空间上得到了新的满足某种Lipschitz型条件的四个映射的唯一公共不动点定理并给出了一些推论.
所得结果推广和改进了文献中一些已知结论.

关键词: TVS -值锥度量空间 , Lipschitz型条件 , 公共不动点.

Abstract:

New unique common fixed point results for four mappings satisfying certain Lipschitz type conditions on a non-complete topological vector space-valued cone metric space are obtained, and their corollaries are given. Our main results generalize and improve some well-known recent results in the literatures.

Key words: TVS-valued cone metric space , Lipschitz type condition , Common fixed point

中图分类号:

47H05

朴勇杰, 金海兰, 金元峰. TVS -值锥度量空间上四个映射的唯一公共不动点[J]. 数学物理学报, 2015, 35(1): 172-181.

PIAO Yong-Jie, JIN Hai-Lan, JIN Yuan-Feng. Unique Common Fixed Points for Four Mappings on |TVS-Valued Cone Metric Spaces[J]. Acta mathematica scientia,Series A, 2015, 35(1): 172-181.

参考文献

[1] Huang L G, Zhang X. Cone metric spaces and fixed point theorems of contractive mappings. J Math Anal Appl, 2007, 332(2): 1468--1476

[2] Abbas M, Jungck G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J Math Anal Appl, 2008, 341(1): 416--420

[3] Abbas M, Rhoades B E. Fixed and periodic point results in cone metric spaces. Applied Math Letters, 2009, 22(4): 511--515

[4] Raja P, Vaezpour S M. Some extensions of Banach's contraction principle in complete cone metric spaces. Fixed Point Theory and Applications, 2008, ID 768294, 11 pages

[5] Kadelburg Z, Radeno\'{v}ic S, Rosi\'{c} B. Strict contractive conditions and common fixed point theorems in cone metric spaces. Fixed Point Theory and Applications, 2009, ID 173838, 14 pages

[6] Jungck G, Radeno\'{v}ic S,Radoje\'{v}ic S, Rako\u{c}evi\'{c} V.Common fixed point theorems for weakly compatible pairs on cone
metric spaces. Fixed Point Theory and Applications, 2009, ID 643840, 13 pages

[7] Ili\'{c} D, Rako\u{c}evi\'{c} V. Quasi-contraction on a cone metric space. Applied Math Letters, 2009, 22(5): 728--731

[8] Janko\'{v}ic S, Kadelburg Z,Radeno\'{v}ic S, Rhoades B E. Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces. Fixed Point Theory and Applications, 2009, ID 7610386, 16 pages

[9] Ismat Beg, Akbar Azam, Muhammad Arshad. Common fixed points for mapps on topological vector space valued cone metric spaces. Inter J Math and Math Sci, 2009, ID 560264

[10] Akbar Azam, Ismat Beg, Muhammad Arshad. Fixed point in topological vector space valued cone metric spaces. Fixed Point Theory and Applications, 2010, ID: 604084

[11] Kadelburg Z, Radenovi\'{c} S, Rako\v{c}evi\'{c} V. Topological vector space valued cone metric spaces and fixed point theorems. Fixed Point Theory and Applications, 2010, ID: 170253, 18p

[12] Karapinar E, Yuksei U. On common fixed point theorem without commuting conditions in TVS-cone metric spaces.J Comput Anal Appl, 2011, 13: 1123--1131

[13] 张宪.锥度量空间中Lipschitz型映射的公共不动点定理. 数学学报, 2010, 53(6): 1139--1148

[14] Abbas M, Jungck G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces. Journal of Mathematical Analysis and Applications,2008, 341(1): 416--420

[15] Han Y, Xu S Y. New common fixed point results for four maps on cone metric spaces. Applied Mathematics,2011, 2: 1114--1118

[16] Bari C D, Vetro P. $\phi$-Pairs and common fixed points in cone metric spaces. Rendiconti del circolo Matematico Palermo, 2008, 57: 279--285