[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()

完备度量空间中的不动点

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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

完备度量空间中的不动点

Author(s):

Zhu Shunrong

Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China

朱顺荣

南京理工大学应用数学系, 南京 210094

Keywords:

fixed point;  complete metric space;  w-distance

不动点;  完备度量空间;  w-距离

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.

使用w-距离概念, 证明了在2个完备度量空间中2个新的不动点定理, 其中之一的结果为: 设(X, d)和(Y, ρ)是2个完备度量空间, 设p₁是X上w-距离和p₂是Y上w-距离. 如果T是一个从X到Y的连续映射和S是一个从Y到X的映射, 对X中所有x, x′ 和Y中所有y, y′以及o<c<1, 满足不等式p₁(STx, STx′)≤cmax{p₁(x, x′), p₁(x, STx), p₁(x′, STx′), p₁(x, STx′)/2, p₂(Tx, Tx′)}和p₂(TSy, TSy′)≤cmax{p₂(y, y′), p₂(y, TSy), p₂(y′, TSy′), p₂(y, TSy′)/2, p₁(Sy, Sy′)}. 证明了ST在X中有惟一不动点z和TS在Y中有惟一不动点w. 这2个定理推广了 Fisher和Namdeo等人的不动点定理.

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.

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