Acta mathematica scientia, Series B >
APPROXIMATING SOLUTION OF 0 ∈T(x) FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES
Received date: 2011-10-27
Revised date: 2012-12-14
Online published: 2013-09-20
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).
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.
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 . DOI: 10.1016/S0252-9602(13)60086-7
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