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

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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.

Keywords

General H-monotone
Proximal mapping
Iterative algorithm
Uniformly smooth Banach space

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This work was supported by the National Natural Science Foundation of China (10671135), the Applied Research Project of Sichuan Province (05JY029-009-1) and the Educational Science Foundation of Chongqing (KJ051307).