AN ITERATIVE ALGORITHM FOR A SYSTEM OF GENERALIZED IMPLICIT NONCONVEX VARIATIONAL INEQUALITY PROBLEMS

K.R.  KAZMI; M.I.  BHAT; NAEEM  AHMAD

Authors

K.R. KAZMI Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
M.I. BHAT Department of Mathematics, South Campus, University of Kashmir, Fetehgarh, Anantnag-192101, Jammu and Kashmir, India
NAEEM AHMAD Department of Mathematics, P.O. Box 2014, Skaka, Al-Jouf University, Kingdom of Saudi Arabia

Keywords:

System of generalized implicit nonconvex variational inequality problems, uniformly prox-regular set, projection method, iterative algorithm, strongly monotone mapping, relaxed-Lipschitz continuous mapping

Abstract

In this paper, we consider a new system of generalized implicit nonconvex variational inequality problems in the setting of two different Hilbert spaces. Using projection method, we establish the equivalence between the system of generalized implicit nonconvex variational inequality problems and a system of nonconvex variational inequality inclusions. Using this equivalence formulation, we suggest an iterative algorithm and show that the sequences generated by this iterative algorithm converge strongly to a solution of the system of generalized implicit nonconvex variational inequality problems. The results presented in this paper can be viewed as an improvement and refinement of previously known results for nonconvex (convex) variational inequality problems.