Variational inclusions with a general H-monotone operator in Banach spaces

Authors:
Fu-Quan Xia;Nan-Jing Huang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

In this paper, we introduce a new class of operator-general H-monotone operators in Banach space. We define a proximal mapping associated with the general H-monotone operator and show its Lipschitz continuity. We also consider a new class of variational inclusions involving these general H-monotone operators and constructed a new iterative algorithm for solving the variational inclusion in Banach spaces. Under some suitable conditions, we prove the convergence of the iterative sequence generated by the algorithm.