Existence Of Solution And Its Algorithm For Vector Equilibrium Problem

In this thesis,we discuss the vector equilibrium problem and obtain the main results of existence,iterative algorithm and its convergence analysis.These results not only promote and develop some relevant research achievements in recent literatures,but also enrich the theory and algorithm of vector equilibrium,and provide important theoretical basis for the practical application of vector equilibrium in economy,production and life.The paper is divided into four chapters,which are as follows:In the first chapter,we mainly summarize the history and present situation of vector equilibrium problems.Then,we introduce the problems to be studied in this paper and state the significance of these studies.In the last section of this chapter,some notations are recalled.Several well-known conclusions are given.In the second chapter,we mainly discuss the existence of solutions for vector equilibrium problems.Under the condition of cosmically upper continuity of the cone-valued mapping,existence theorems of two kinds of vector quasi-equilibrium problems with variable domain structure(control structure)are obtained by using the Fan-KKM theorem and the Kakutani-Fan-Glicksberg fixed point theorem.Further,a concrete example is given to illustrate the validity of the results.In the third chapter,in order to discuss the algorithm of vector equilibrium problem,we firstly introduce an auxiliary problem for the strong vector equilibrium problem and discusse the relationships between the auxiliary problem and the original vector equilibrium problem.Furthermore,an existence theorem of solution for the auxiliary problem is given.Then,on the basis of the auxiliary problem,a general iterative algorithm for solving the strong vector equilibrium problem is given and the convergence of the algorithm is studied indetail under some appropriate conditions of cone continuity and cone convexity.In the fourth chapter,we summarize the results and conclusions obtained in this thesis and puts forward a new prospect.