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[1] Zhu Shunrong,. Fixed points on complete metric spaces [J]. Journal of Southeast University (English Edition), 2004, 20 (2): 256-260. [doi:10.3969/j.issn.1003-7985.2004.02.027]
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Fixed points on complete metric spaces()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 2
Page:
256-260
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-06-30

Info

Title:
Fixed points on complete metric spaces
Author(s):
Zhu Shunrong
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
Keywords:
fixed point;  complete metric space;  w-distance
PACS:
O174.12
DOI:
10.3969/j.issn.1003-7985.2004.02.027
Abstract:
Two new fixed point theorems on two complete metric spaces are proved by using the concept of w-distance. One of the results is: let (X, d) and (Y, ρ) be two complete metric spaces, let p1 be a w-distance on X and p2 be a w-distance on Y. If T is a continuous mapping of X into Y and S is a mapping of Y into X, satisfying the inequalities: p1(STx, STx′)≤cmax{p1(x, x′), p1(x, STx), p1(x′, STx′), p1(x, STx′)/2, p2(Tx, Tx′)} and p2(TSy, TSy′)≤cmax{p2(y, y′), p2(y, TSy), p2(y′, TSy′), p2(y, TSy′)/2, p1(Sy, Sy′)} for all x, x′ in X and y, y′ in Y, where 0≤c<1. We have proved that ST has a unique fixed point z in X and TS has a unique fixed point w in Y. The two theorems have improved the fixed point theorems of Fisher and Namdeo, et al.

References:

[1] Jeong S U. Note fixed point theorems related to C′iric′s contraction principle [J]. J Math Anal Appl, 1998, 225(2): 630-640.
[2] Kada O, Suzuki T, Takahashi W. Nonconvex minimization theorems and fixed point theorems in complete metric spaces [J]. Math Japonica, 1996, 44(2): 381-391.
[3] Fisher B. Related fixed points on two metric spaces [J]. Math Sem Notes Kobe Univ, 1982, 10(1): 17-26.
[4] Namdeo R K, Tiwari N K, Fisher B, et al. Related fixed point theorems on two complete and compact metric spaces [J]. Int J Math Sci, 1998, 21(3): 559-563.
[5] Jungck G. Commuting mappings and fixed points [J]. Amer Math Monthly, 1976, 83(4): 261-263.

Memo

Memo:
Biography: Zhu Shunrong(1946—), male, professor, zhushr@mail. njust. edu. cn.
Last Update: 2004-06-20