Proximal point algorithm with errors for generalized strongly nonlinear quasivariational inclusions

In this paper, a class of generalized strongly nonlinear quasivariational inclusionsare studied. By using the properties of the resolvent opera for associated with amaximal monotone mapping in Hilbert space, an existence theorem of solutions forgeneralized strongly nonlinear quasi variational inclusion is established and a newproximal point algorithm with errors is suggested for finding approximate solutionswhich strongly converge to the exact solution of the generalized strongly nonlinearquasivariational inclusion. As special cases, some known results in this field are alsodiscussed.