| The fixed point theory of nonlinear operators is an important part of nonlinear functional analysis. Especially, the studying of iterative algorithm for solutions of nonlinear operator equations becomes the focus of attention in this field recently.The thesis centers upon the existence and uniqueness of fixed point or common fixed point about (?)-contraction type mappings,compatible mappings,Altman mappings of integral type, (Ag) type compatible mappings and trace contractive type mappings,centers upon using iterative algorithm to fingd a common element of the set of fixed points of a nonexpansive mapping,the set of solutions of variational inequality and the set of solutions of an equilibrium problem. The integrated thesis consists of four parts. The preface is to show the background and current situation about the theory of fixed points and nonlinear operators. In the first chapter, we discuss some common fixed point problems for compatible andsubcompatible mappings of(?)-contraction type,compatible mappings,Altman compatable mappings of integral type in complete metric spaces. In the second chapter, we are concerned about some fixed point problems of trace contractive type mappings and common fixed point problems of (Ag)type(?)-weak commutativity noncompatible mappings in metrical spaces. In the last chapter, introducing a compond iterative algorithm to study the convergence problems of common element of the set of fixed points of a nonexpansive mapping,the set of solutions of variational inequality and the set of solutions of an equilibrium problem in a Hilbert space.In a word, in this paper, we obtain some fixed point,conmmon fixed point and iterative convergence theorems by introducing new class of mappings and new iteration scheme and using new iteration techniques. The results presented in this paper are generalizations,extensions and improvements of the corresponding known ones. Hence the theory of fixed points and nonlinear operators is enriched and developed. |
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