Iterative Methods Of Common Fixed Points For Several Families Of Nonlinear Mappings

Iterative algorithms of fixed points for nonlinear mappings are currently active research subjects in the field of nonlinear functional analysis. Several new composite iterative algorithms are proposed to approximate common fixed points of a family of strictly quasi-pseudocontractive mappings, a family of Lipschitz quasi-pseudocontractive mappings and a family of quasi --φ strictly asymptotically pseudo-contractive mappings respectively in this thesis. Several strong convergence theorems of common fixed points are proved by using new analysis techniques. The results of this paper improve and extend recent some relative result. The main content of this paper is as follows:In the first part, a new composite iterative algorithm is proposed to approximate common fixed points of a family of strictly quasi-pseudocontractive mappings. A strong convergence theorem of common fixed points is proved by using the properties of the norm, the condition(Z) and the properties of metric projections in the framework of Hilbert spaces.In the second part, a new hybrid projection method is proposed to approximate common fixed points of a family of Lipschitz quasi-pseudocontractive mappings. A strong convergence theorem of common fixed points is proved by using the proposed algorithm and the properties of metric projections in the framework of Hilbert spaces.In the third part, a hybrid projection algorithm is proposed to approximate common fixed points of a family of quasi --φ strictly asymptotically pseudo-contractive mappings. Under the condition of removing the boundedness of the set C, a strong convergence theorem of common fixed points is proved by using the normalized duality mapping, the property(K) and the generalized projection in the framework of reflexive, strictly convex and smooth Banach spaces.