Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 59836, 12 pages
doi:10.1155/JIA/2006/59836

On multivalued nonlinear variational inclusion problems with (A,η)-accretive mappings in Banach spaces

Heng-You Lan

 Department of Mathematics, Sichuan University of Science & Engineering, Zigong 643000, Sichuan, China
Received 20 January 2006; Revised 12 May 2006; Accepted 15 May 2006

Abstract

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 problems with (A,η)-accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear 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.