ISHAKAWA TYPE ITERATIVE ALGORITHM FOR NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE MAPPINGS
This work was supported by the State 863 Program (2003AA148040), the National Natural Science Foundation of China (grant number 10471151,60216263, 6990312) and the Educational Science Foundation of Chongqing, Chongqing of China (KJ051307).
In this paper, we introduce a new class of nonlinear variational inclusions with H-monotone mappings. By using the resolvent operator method associated with H-monotone mappings in Hilbert spaces, we prove the existence and uniqueness of solution for this class of nonlinear variational inclusions. We also construct a new Ishikawa type iterative algorithm for finding approximate the solution of this nonlinear variational inclusion and discuss the convergence and stability of sequence of iterates generated by the algorithm. The present results improve and extend many known results in the literature.
