Existence Of Fixed Point For Nonlinear Operators And Iterative Convergence

Existence of fixed point for nonlinear operators and iterative convergence are importantparts of nonlinear functional analysis, and they have become the topic that people studyin the recently years. In this paper, we mainly study the following nonlinear operators:mixed monotone operators, relaxed (γ,r)-cocoercive operators and W-operators. This paperincludes four chapters. Now we will describe them brie?y one by one.Chapter 1 recalls the history and present situation of existence of fixed point for nonlin-ear operators and iterative convergence and we also give a summary of this work.Chapter 2 mainly concerns about the existence of fixed point for mixed monotone op-erators in cone.Chapter 3 mainly considers convergence analysis for a family of finite equilibrium prob-lems and fixed point problems of relaxed (γ,r)-cocoercive operators in Hilbert spaces.Chapter 4 mainly discusses about the convergence problems of a general iterative pro-cess for W-operators in Hilbert spaces.