Discussion Of Related Problems Of Fixed Point Theory

The fixed point’s proposion promotes mathematics and physics fields’develop-ment. So it’s paid more attention in the field of fixed point theory. People use different iterative algorithm to study nonlinear mapping’s approximate fixed point, and then solve some actual problems in these fields. The core problem is researching iterative algorithm’s strong or weak convergence. Besides, we could consider that several problems are studied together, so we can get some good conclusions. In the paper, for common fixed point of different mappings and their applications, we mainly study problems as follow:一、Strong convergence.(1) Strong convergence of nonexpansive mapping’iterative algorithm;(2) Strong convergence of common fixed point of nonexpansive mapping and uniformly L-Lipschitzian mapping’iterative algorithm;(3) Strong convergence of common fixed point of weak relatively nonexpansive mappings’iterative algorithm.二、Some application.Consider common solutions of equilibrium problem and variational problem in the previous research on iterative algorithm, combine common fixed point of different mappings, generalized equilibrium problem with variational problem, and then new iterative algorithm is proposed. And I get some conclusions.