(H(·,·),η)-accretive operators with an application for solving set-valued variational inclusions in Banach spaces

Authors:
Zhong Bao Wang;Xie Ping Ding
Affiliations:
Mathematical College, Sichuan University, Sichuan, Chengdu, 610064, PR China;College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, we introduce a new class of accretive operators-(H(@?,@?),@h)-accretive operators, which generalize many existing monotone or accretive operators. The resolvent operator associated with an (H(@?,@?),@h)-accretive operator is defined and its Lipschitz continuity is presented. By using the new resolvent operator technique, we also introduce and study a new class of set-valued variational inclusions involving (H(@?,@?),@h)-accretive operators and construct a new algorithm for solving this class of set-valued variational inclusions. These results are new, and improve and generalize many known corresponding results.