Some Problems For Iterative Algorithms Of Accretive Mappings, Pseudo-Contractive Mappings And Variational Inclusions

The concepts of accretive mapping and pseudo-contractive mapping wereintroduced by the studying of nonlinear evolution equations,many significantproblems and engineer problems can be modeled in terms of the form.In this paper, we mainly study some problems for iterative approximations offixed points involving accretive mappings and pseudo-contractive mappings,and alsowe discuss the iterative approximation problem of solution to generalized set-valuedvariational inclusions.Our results improve and generalize many known results.Thisthesis is divided into the following six sections.In first section, the background of the iterative approximations of fixed pointsfor accretive mappings and pseudo-contractive mappings is introduced briefly.In second section, some notions and conclusions in this paper have beenreviewed.In third section, a characteristic condition is given for a generalized steepestdecent method to converge to the zeros of quasi-accretive operator.In fourth section, generalizedΦ-pseudo-contractive type mappings areintroduced.The iterative convergence problems of the mappings are proved.In fifth section, the iterative algorithms of asymptotically pseudo-contractivemappings in Banach spaces are discussed.In sixth section, the exist theorem and convergence theorem of the solutions togeneralized set-valued variational inclusions are proved.