Strong convergence of an iterative method for variational inequality problems and fixed point problems

摘要: In this paper, we introduce a general iterative scheme to investigate the problem of finding common element fixed point set strict pseudocontraction and solution variational inequality for relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in real Hilbert space. 1. Introduction preliminaries Variational inequalities introduced Stampacchia (16) early sixties have had great impact influence development almost all branches pure applied sciences witnessed an explosive growth theoretical advances, algorithmic development, see (4)-(22) references therein. consider approximation solutions classical Let H be space, whose inner product norm denoted h·,·i andk·k, C nonempty closed convex subset A: C! nonlinear mapping.