International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 17-20, Pages 1035-1045
doi:10.1155/S0161171204308069
An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces
A.H. Siddiqi1
and Rais Ahmad2
1Department of Mathematical Sciences, King Fahd University of Petroleum \& Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Abstract
We use Nadler's theorem and the resolvent operator technique for m-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.