GENERAL FRAMEWORK FOR A SUPER-RELAXED PROXIMAL POINT ALGORITHM AND ITS APPLICATIONS TO BANACH SPACES

Abstract

Based on the notion of A-maximal relaxed accretiveness, rst a general framework for a super-relaxed proximal point algorithm is introduced, and then the convergence analysis for the algorithm to the context of approximating solutions to a class of nonlinear inclusion problems is examined along with some auxiliary results on the generalized resolvent operator corresponding to A-maximal relaxed accretiveness. The A-maximal relaxed accretiveness seems to be applicable generalizing results on the theory of hemivariational inequalities that is a direct generalization to variational inequalities. As a matter of fact, hemivariational inequalities arise from mechanics, engineering sciences, economics relating to nonconvex energy functionals or equivalently relating to nonmonotone possibly multivalued laws, for instance between stresses and strains or reactions and displacements in deformable bodies between heat flux and temperature in thermal problems or between dierential and flow intensities in economic network problems.