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

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

Abstract

Abstract:

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.

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

CLC Number:

47H05

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

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