Algorithm Study Of Split Equilibrium Problem And General Split Equality Variational Inclusion Problems

The split equilibrium problem is promotion of nonlinear problems and applicates in a large variety of problems arising in numerous problems in economics,physics.The general split equality variational inclusion problems is promotion of the split feasibility problem.The split feasibility problem be used in various disciplines such as image restoration,computer tomograph and radiation therapy treatment planning.So it is very meaningful to study the split equilibrium problem and split equality variational inclusion problems.In this paper,we mainly study the algorithm of split equilibrium problem and general split equality variational inclusion problemsThis thesis consists of five chapters.In chapter 1,we briefly introduce the research background,current situation and research content of split equilibrium problem and general split equality variational inclusion problems.In chapter 2,we introduce the related definitions and lemma of split equilibrium problem and general split equality variational inclusion problems.In chapter 3,we study split equilibrium problems and fixed point problems for nonspreading multi-valued mappings in Hilbert space.We suggest a new iterative scheme for solving the split equilibrium problems and fixed point problems of (?)-nonspreading multivalued mappings in Hilbert spaces.We also show that the iteration converges strongly to a common solution of the considered problems.Finally,a numerical example is illustrated to verify the validity of the proposed algorithm.In chapter 4,we study general split equality variational inclusion problems in Banach spaces.We suggest a new iterative scheme for solving general split equality variational inclusion problems in Banach spaces.We also show that the iteration converges strongly to a common solution of the general split equality variational inclusion problems(GSEVIP).In chapter 5,we make a brief summary for this paper and introduce our future work.