| 文萌,胡长松,彭济根.q-一致光滑和严格凸的Banach空间中的无穷个严格伪压缩映射的混合迭代算法[J].数学年刊A辑,2014,35(4):485~500 |
| q-一致光滑和严格凸的Banach空间中的无穷个严格伪压缩映射的混合迭代算法 |
| A General Composite Iterative Algorithm for an Infinite Family of Strictly Pseudo-Contractive Mappings in q-Uniformly Smooth and Strictly Convex Banach Spaces |
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| DOI： |
| 中文关键词: 投影, 严格伪压缩映射, 不动点, $k$-李普希兹, $\eta$-强单调 |
| 英文关键词:Projection, Strictly pseudo-contractive mappings, Fixed point, $k$-Lipschitzian, $\eta$-strongly monotone |
| 基金项目:国家自然科学基金 (No.11131006, No.60970149) 和陕西省教育厅科研计划项目 |
| Author Name | Affiliation | E-mail | | WEN Meng | School of Mathematics and Statistics, Xi'an Jiaotong University,
Xi'an 710049, China. | wen5495688@163.com | | HU Changsong | Department of Mathematics, Hubei Normal University, Huangshi 435002, Hubei, China. | huchang1004@yahoo.com.cn | | PENG Jigen | School of Mathematics and Statistics, Xi'an Jiaotong University,
Xi'an 710049, China. | jgpeng@mail.xjtu.edu.cn |
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| 中文摘要: |
| 在$q$-一致光滑和严格凸的Banach空间中, 研究了无穷个严格伪压缩映射的混合迭代算法, 证明了由这种新的算法产生的序列强收敛于这无穷个严格伪压缩映射的公共不动点
, 并且是变分不等式 $\langle(I -A)\wt{x}, J_{q}(p-\wt{x})\rangle\leq0$, $p \in \bigcap\limits_{i=1}^{\infty}F(T_{i})$的解.
论文推广和改进了一些前人的相应结论. |
| 英文摘要: |
| The authors consider a general composite iterative
method for obtaining an infinite family of strictly
pseudo-contractive mappings in $q$-uniformly smooth and strictly
convex Banach spaces. It is proved that the sequence generated by
the iterative scheme converges strongly to a common point of the set
of fixed points, which solves the variational inequality $\langle(I
-A)\wt{x}, J_{q}(p-\wt{x})\rangle\leq0$ for $p \in
\bigcap\limits_{i=1}^{\infty}F(T_{i})$. The results improve and
extend the corresponding ones announced by some others. |
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