Iterative Apprpximation Problems For The Fixed Point Theory Of Nonlinear Operators And Operator Semigroups

Abstract:The fixed point theory of nonlinear operators is an constituent impor-tant part of nonlinear functional analysis, especially,the problem of approximating to solutions of nonlinear operator equations becomes the topic that people study in the recently years.For a rather long time,many authors have been using Mann iterative methods and hybid projection algorithms for computing solutions to the fixed points of nonlinear operators.In this paper three problems are mainly discussed:Firstly, Let H be a real Hilbert space, C be a nonempty closed convex subset of H , under the condition of original nonexpensive mappings,the concept of semigroups is introduced. The stronge convergence theorems for fixed points of nonexpansive semigroups is obtained by using apprpximation Monotone Hybrid Algorithm.Secondly,defined a new mapping,that is, a family of quasi-nonexpansive map-pings which is established on the basis of original quasi-nonexpansive mappings, the common fixed points are finded by using the modified hybrid projection algo-rithms,The strong convergence theorems of the iterative sequuence are obtained.Finally, asymptotically nonexpensive mappings and asymptoticallyκ-strict pseudo contractions Mappings are extended to a family of operators.Modified hybrid projec-tion algorithms is constructed for finding a common fixed points of a family of asymp-totically nonexpensive mappings and asymptoticallyκ-strict pseudo-contractions Map- pings.The strong convergence theorems of the iterative sequuence are obtained.