A new class of variational inclusions with BB-monotone operators in Banach spaces

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of BB-monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the BB-monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm.