APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

doi:10.1016/S0252-9602(13)60086-7

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1347-1360.doi: 10.1016/S0252-9602(13)60086-7

APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

刘三洋*|贺慧敏|陈汝栋

Department of Mathematics, Xidian University, Xi´an 710071, China|Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

收稿日期:2011-10-27 修回日期:2012-12-14 出版日期:2013-09-20 发布日期:2013-09-20
通讯作者: 刘三洋，liusanyang@126.com E-mail:liusanyang@126.com; huiminhe@126.com; chenrd@tjpu.edu.cn
基金资助:
This work was supported by National Science Foundation of China (11071279), National Science Foundation for Young Scientists of China (11101320 and 61202178), and the Fundamental Research Funds for the Central Universities (K5051370004, K50511700007).

APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

LIU San-Yang*, HE Hui-Min, CHEN Ru-Dong

Department of Mathematics, Xidian University, Xi´an 710071, China|Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received:2011-10-27 Revised:2012-12-14 Online:2013-09-20 Published:2013-09-20
Contact: LIU San-Yang，liusanyang@126.com E-mail:liusanyang@126.com; huiminhe@126.com; chenrd@tjpu.edu.cn
Supported by:
This work was supported by National Science Foundation of China (11071279), National Science Foundation for Young Scientists of China (11101320 and 61202178), and the Fundamental Research Funds for the Central Universities (K5051370004, K50511700007).

摘要/Abstract

摘要：

The purpose of this paper is to study the solution of 0 ∈ T(x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first proposal of it´s kind. Some strong and weak convergence results are presented and the relations between maximal monotone operators and H-monotone operators are analyzed. Simultaneously, we apply these results to the minimization problem for T = ∂f and provide some numerical examples to support the theoretical findings.

关键词: H-monotone operators, inclusion problem 0∈T(x), resolvent operator, strong convergence, weak convergence

Abstract:

Key words: H-monotone operators, inclusion problem 0∈T(x), resolvent operator, strong convergence, weak convergence

中图分类号:

47H05

刘三洋, 贺慧敏, 陈汝栋. APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES[J]. 数学物理学报(英文版), 2013, 33(5): 1347-1360.

LIU San-Yang, HE Hui-Min, CHEN Ru-Dong. APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES[J]. Acta mathematica scientia,Series B, 2013, 33(5): 1347-1360.

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APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

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