Banach空间中含$(\emph{\textbf{H}},\bm\phi)$-$\bm\eta$-单调算子的变分包含组

华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (1): 74-83.

Banach空间中含$(\emph{\textbf{H}},\bm\phi)$-$\bm\eta$-单调算子的变分包含组

张超

淮南师范学院数学与计算科学系, 安徽淮南 232001

收稿日期:2011-04-01 修回日期:2011-07-01 出版日期:2012-01-25 发布日期:2012-01-26

System of variational inclusions with ${(\emph{\textbf{H}},{\bm\phi})}$-$\bm\eta$-monotone operators in Banach spaces

ZHANG Chao

Department of Mathematics and Computational Science, Huainan Normal University, Huainan Anhui 232001, China

Received:2011-04-01 Revised:2011-07-01 Online:2012-01-25 Published:2012-01-26

摘要/Abstract

摘要： 在实的一致光滑Banach空间中, 引入一类新的含$(H,\phi)$-$\eta$-单调算子的变分包含组. 利用$(H,\phi)$-$\eta$-单调算子的近似映射技巧, 证明了此类新的变分包含组解的存在性与唯一性, 并构造了逼近此类变分包含组解的迭代算法; 讨论了由此迭代算法生成的迭代序列的收敛性. 所得结果推广与改进了文献中的一些主要结果.

关键词: $(H,\phi)$-$\eta$-单调算子, 近似映射, 变分包含组, 迭代算法, 收敛性

Abstract: This paper introduced a new system of variational inclusions with $(H,\phi)$-$\eta$-monotone operators in real uniformly smooth Banach spaces. By using the proximal mapping technique associated with $(H,\phi)$-$\eta$-monotone operators, we proved the existence and uniqueness of solution for this new system and construct a new iterative algorithm for approximating the solution of this system. The convergence of the iterative sequence generated by the iterative algorithm was also discussed. The results extend and improve some known results in the literature.

Key words: $(H,\phi)$-$\eta$-monotone operator, proximal mapping, system of variational inclusions, iterative algorithm, convergence

中图分类号:

张超. Banach空间中含$(\emph{\textbf{H}},\bm\phi)$-$\bm\eta$-单调算子的变分包含组[J]. 华东师范大学学报(自然科学版), 2012, 2012(1): 74-83.

ZHANG Chao. System of variational inclusions with ${(\emph{\textbf{H}},{\bm\phi})}$-$\bm\eta$-monotone operators in Banach spaces[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(1): 74-83.

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