Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 709715, 20 pages
http://dx.doi.org/10.5402/2011/709715
Research Article

( 𝐻 , πœ™ ) - πœ‚ -Accretive Mappings and a New System of Generalized Variational Inclusions with ( 𝐻 , πœ™ ) - πœ‚ -Accretive Mappings in Banach Spaces

Department of Mathematics, Yasouj University, Yasouj 75914, Iran

Received 5 June 2011; Accepted 29 June 2011

Academic Editors: Y.-K. Chang and Z. Hou

Copyright © 2011 Sayyedeh Zahra Nazemi. 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.

Abstract

We introduce a new class of generalized accretive mappings, named ( 𝐻 , πœ™ ) - πœ‚ -accretive mappings, in Banach spaces. We define a resolvent operator associated with ( 𝐻 , πœ™ ) - πœ‚ -accretive mappings and show its Lipschitz continuity. We also introduce and study a new system of generalized variational inclusions with ( 𝐻 , πœ™ ) - πœ‚ -accretive mappings in Banach spaces. By using the resolvent operator technique associated with ( 𝐻 , πœ™ ) - πœ‚ -accretive mappings, we construct a new iterative algorithm for solving this system of generalized variational inclusions in Banach spaces. We also prove the existence of solutions for the generalized variational inclusions and the convergence of iterative sequences generated by algorithm. Our results improve and generalize many known corresponding results.