Iterative Algorithm For The Fixed Point Problem Of Strictly Pseudocontractive Mappings

The fixed point theory of nonlinear operations and equilibrium problems are important parts 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. In this paper, we construct effective schemes to approximate the common fixed point of a family ofλi—strictly pseudocontractive mappings and find a common element of the set of common fixed points of a finite family of asymptotically ki—strictly pseudo-contractions in the intermediate sense and the set of solutions of an equilibrium problem. Results presented in this paper improve and extend many authors'recent results. This paper includes fives chapters. Now we will describe them briefly one by one.Chapter 1 recalls the history and present situation of nonlinear operator equations in Banach spaces and we also give a summary of this work.Chapter 2 mainly concerns about the convergence problems of modified Ishikawa iter-ative process with errors for an infinite family of strict pseudocontractions in q—uniformly smooth Banach spaces.Chapter 3 mainly discusses about the convergence problems of a general iterative pro-cess for a finite family ofλi—strict pseudocontractions in q—uniformly smooth Banach spaces.Chapter 4 mainly considers convergence analysis for equilibrium problems and fixed point problems of a finite family of asymptotically ki—strictly pseudocontractive mappings in the intermediate sense in Hilbert spaces.