An extension of a class of iterative procedures for nonlinear quasivariational inequalities
Consider the convergence of the projection methods based on an extension of a special class of algorithms for the approximation-solvability of the following class of nonlinear quasivariational inequality (NQVI) problems: find an element x* is an element of H such that g(x*) is an element of K and   greater than or equal to 0 for all g(x) is an element of K, where T, g : H --> H are mappings on H and K is a nonempty closed convex subset of a real Hilbert space H. The iterative procedure is characterized as a nonlinear quasivariational inequality: for any arbitrarily chosen initial point x(0) is an element of K and, for constants rho > 0 and beta > 0, we have   greater than or equal to 0, for all g(x) is an element of K and for k greater than or equal to 0, where   greater than or equal to 0 for all g(x) is an element of K. This nonlinear quasivariational inequality type algorithm has an equivalent projection formula g(x(k+1)) = P-K[g(y(k)) - rhoT(y(k))], where g(y(k)) = P-K[g(x(k)) - betaT(x(k))], for the projection P-K of H onto K.
projection method approximation-solvability cocoereive mapping