ON MULTIVALUED NONLINEAR VARIATIONAL INCLUSION PROBLEMS WITH (A,η)-ACCRETIVE MAPPINGS IN BANACH SPACES

Based on the notion of (A,η)-accretive mappings and the resolvent operators associated with (A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problemswith (A,η)-accretivemappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlin-ear variational inclusion problems involving (A,η)-accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in q-uniformly smooth Banach spaces. Copyright © 2006 Heng-You Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1