Several Iterative Methods For Fixed Points Of G-nonexpansive Mappings

The fixed point theory of nonlinear operators is a hot topic in the research of nonlinear functional analysis.For a long time,many scholars have devoted themselves to studying the problem of nonlinear operators iteratively approaching fixed points.With the research and development of fixed points,they have begun to study Regarding the fixed point problem of G-nonexpansive mapping,good results have been obtained.The thesis improves and generalizes some of the previous conclusions.Mainly studies the fixed point iterative method of G-nonexpansive mapping in Banach space and the iterative approximation of the common element of the fixed point problem and the zero point problem of the variational inequality problem.The convergence of the iterative sequence generated by this algorithm is proved by constructing a finite step iteration,and give numerical experiments to prove the advantages of this algorithm.The full text is mainly divided into three parts:In the first part,in a uniformly convex Banach space with a directed graph,an SP-iterative method is constructed to approximate the common fixed point of a family of G-nonexpansive mappings.The constructed algorithm is used to prove the strong and weak convergence theorems of the common fixed point.A numerical example is given to verify the advantages of this method.In the second part,in a uniformly convex Banach space with a directed graph,a modified multi-step-iterative method is constructed to prove the strong and weak convergence theorems of the common fixed points of the G-nonexpansive mapping family,and a numerical example is given to verify the method the advantages.In the third part,in a strictly convex uniformly smooth Banach space with K-K properties,A new contraction projection iterative method is designed to approximate the common elements of the fixed point set of the semi-relatively nonexpansive mapping,the zero point set of the maximal monotone operator,and the solution set of the variational inequality problem,and the designed algorithm is used to prove The strong convergence theorem of the common element.