On multivalued nonlinear variational inclusion problems with Open image in new window -accretive mappings in Banach spaces
Based on the notion of Open image in new window -accretive mappings and the resolvent operators associated with Open image in new window -accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with Open image in new window -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving Open image in new window -accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in Open image in new window -uniformly smooth Banach spaces.
KeywordsBanach Space Iterative Algorithm Variational Inclusion Smooth Banach Space Inclusion Problem
- 2.Fang Y-P, Cho YJ, Kim JK: -accretive operators and approximating solutions for systems of variational inclusions in Banach spaces. to appear in Nonlinear Analysis to appear in Nonlinear AnalysisGoogle Scholar
- 4.Fang Y-P, Huang N-J: Approximate solutions for nonlinear operator inclusions with-monotone operators. In Research Report. Sichuan University, Chengdu; 2003.Google Scholar
- 11.Lan H-Y, Cho YJ, Verma RU: On nonlinear relaxed cocoercive variational inclusions involving-accretive mappings in Banach spaces. to appear in Computers & Mathematics with Applications to appear in Computers & Mathematics with ApplicationsGoogle Scholar
- 15.Verma RU: Approximation-solvability of a class of-monotone variational inclusion problems. Journal of the Korean Society for Industrial and Applied Mathematics 2004,8(1):55–66.Google Scholar
This article is published under license to BioMed Central Ltd. 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.