International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 20, Pages 1035-1045
An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly
accretive mappings in Banach spaces
1Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Received 7 August 2003
Copyright © 2004 A. H. Siddiqi and Rais Ahmad. 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.
We use Nadler's theorem and the resolvent operator technique for
-accretive mappings to suggest an iterative algorithm for
solving generalized nonlinear variational inclusions with relaxed
strongly accretive mappings in Banach spaces. We prove the
existence of solutions for our inclusions without compactness
assumption and the convergence of the iterative sequences
generated by the algorithm in real Banach spaces. Some special
cases are also discussed.