Sumeera Shafi - Department of Mathematics, S.P. College, Cluster University, Srinagar-۱۹۰۰۰۱, India

In this paper, we introduce and study a system of generalized quasi-variational inequalities involving nonlinear, nonconvex and nondifferentiable terms in uniformly smooth Banach space. By means of the retraction mapping technique, we prove the existence of solutions for this system of quasi-variational inequalities. Further, we suggest an iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the iterative algorithm under some suitable conditions.

System of generalized quasi-variational inequalities, Nonlinear, nonconvex and nondifferentiable term, uniformly smooth Banach space, retraction mapping, iterative algorithm, Convergence analysis