概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理<sup>*</sup>

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理^*

基金项目: *国家自然科学基金资助课题

摘要: 借助偏序方法,本文得到概率度量空间中之一推广形式的Ekeland变分原理及一集值形式的Caristi重合定理,同时证明了这两个定理之间的等价性.本文结果是[1,2,5,6,7,9]中相应结果的改进和推广.
- 概率度量空间 /
- Caristi重合定理 /
- Ekeland变分原理 /
- 偏序集
Abstract: By using the partial ordering method,a more general type,of Ekeland's variational principle and a set-valued Caristi's coincidence theorem in probabilistic metric spaces are obtained.In addition,we give a simple direct proof of the equivalence between these two theorems in probabilistic metric spaces.
- probabilistic metric space /
- Caristi’s coincidence theorem /
- Ekeland’s variational principle /
- partial ordering set

[1]	Caristi,J.,Fixed point theorem for mappings satisfying inwardness conditions,Trans.Amer.Math.Soc.,215(1976),241-251.
[2]	Ekeland,I.,Nonconvex minimization problems,Bull.Amer.Math.Soc.(New Series),1(1979),443-474.
[3]	Schweizer,B.and A.Sklar,Statistical metric spaces,Pacific J.Math.,10,(1960),313-334.
[4]	Schweizer,B.,A.Sklar and E.Thorp,The metrization of statistical metric spaces,Pacific J.Math.,10(1960),673-675.
[5]	Zhang Shi-sheng and LuoQun,Set-valued Caristi's fixed point theorem and Ekeland's variational principle,Applied Math,and Mech.,10,2(1989),119-121.
[6]	Zhang Shi-sheng,Chen Yu-qing and Guo Jin-li,Ekeland's variational principle andCaristi's fixed point theorem in probabilistic metric spaces,Acta Math.Appl.Sinica,3(1991).
[7]	史树中,Ekeland变分原理与Caristi不动点定理的等价性,数学进展,16(1987),203-206.
[8]	张石生,《不动点理论及应用》,重庆出版社(1984).
[9]	Park,S.,J.Korean Math.Soc.,19(1983),143-151.

点击查看大图