Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 96012, 16 pages
doi:10.1155/FPTA/2006/96012

Convergence and stability of a three-step iterative algorithm for a general quasi-variational inequality problem

K. R. Kazmi1 and M. I. Bhat1,2

 1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Applied Mathematics, Baba Ghulam Shah Badshah University, Jammu and Kashmir, Rajouri, India
Received 11 February 2005; Revised 10 September 2005; Accepted 13 September 2005

Abstract

We consider a general quasi-variational inequality problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The theorems presented in this paper generalize, improve, and unify many previously known results in the literature.