Extra-Gradient Methods For Solving Split Feasibility And Fixed Point Problems

In real Hilbert space,SFP,FPP and SFP-FPP are used to represent split-feasible problem,fixed point problem,split-feasible and fixed point problem respectively;EGIA is also used to represent the external gradient selection algorithm.The modified Mann-Ishikawa EGIA to solve the problem of SFP-FPP with pseudo compressed image is taken as the reserch standard.A modified Ishikawa EGIA is proposed to solve the SFP-FPP with Lipschitz continuous compression image.Secondly,a modified Mann EGIA is proposed to solve the SFP-FPP of pseudo-compressed images without Lipschitz conditions.Under appropriate constraints,we prove that the sequences generated by the proposed generation algorithm converge weakly to the solutions of SFP-FPP by virtue of the properties of projection operators and pseudo-compressed images.The theorems obtained in this paper are improved and develop some corresponding results in the literature.The paper is divided into two parts.The first part introduces the research background and development status of the SFP-FPP,gives the knowledge points needed in convergence analysis,and summarizes the main work of this paper.In the second part,we use Ishikawa-type EGIA to solve the SFP-FPP involved in pseudo-contractive mappings with Lipschitz assumption,and prove that the sequences generated by these substitution algorithms converge weakly to a solution of the SFP-FPP.In chapter three,the Mann type EGIA is used to solve the SFP-FPP involved in pseudo-contractive mappings with Lipschitz assumption,and a solution of the weak convergence of sequences generated by these substitution algorithms to the SFP-FPP is proved.Finally,chapter four gives the conclusion and prospect.