General Iterative Algorithms For Common Solutions Of Equilibrium Problem And Fixed Point Problem And Convex Optimization Problem

As an useful tool, fixed point theory plays an important rool in sloving equilibrium and optimization problems. This paper study equilibrium and strict pseudo-contraction fixed point iteration problems, proposed two composite iterative algorithms, to approximate the common solution of the above two problems. Based on G. Matino and Xu’s algorithm, we proposed the implicit and explicit composite iterative algorithm, to approximate the common solution of equilibrium and constrained convex optimization problems. This paper includes three sections:Chapter1recalls the history and present situation of iteration algorithms for solving fixed point problems of nonlinear operators, and we also give a summary of author’s work.Chapter2based on Tian’s result, given a new composite iterative scheme to approximate the common solution of equilibrium and fixed point of strict pseudo-contrative mapping problems. Under sutiable conditions, strong convergence theorems are obtained.Chapter3based on Marino and Xu’s result, combine the gradient-projection algorithm and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of equilibrium and constrained convex minimization problems. Under sutiable conditions, strong convergence theorems are obtained.