ITERATIVE ALGORITHM FOR A SYSTEM OF MULTI-VALUED VARIATIONAL INCLUSIONS INVOLVING $(B, \phi)$-MONOTONE MAPPINGS IN BANACH SPACES
In this paper, we introduce a new class of resolvent mappings for $(B, \phi)$-monotone mappings in Banach space, which is a natural and important generalization of a class of resolvent mappings studied in [X.-P. Luo, N.-J. Huang; A new class of variational inclusions with B-monotone operators in Banach spaces, J. Comput. Appl. Math. 233 (2010), 1888-1896]. We study some properties of this new class of resolvent mappings and by making use of it, we discuss the existence and iterative approximation of solutions of a system of multi-valued variational inclusions. The method and results presented in this paper improve and generalize many known results in the literature.
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