A PROXIMAL POINT ALGORITHM FOR SOLVING THE GENERAL VARIATIONAL INCLUSIONS WITH M(·, ·)-MONOTONE OPERATORS IN BANACH SPACES

In this paper, a new monotonicity, M(·,·)-monotonicity, is introduced in Banach spaces, and the resolvent operator of an M(·,·)-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·,·)-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.