Existence Of Solutions For Vector Equilibrium Problems In Cone B-metric Spaces

Vector equilibrium problems and the system of vector equilibrium problems are widely used in real life,moreover,Ekeland's variational principle is very important for the study of equilibrium theory.In this paper,we study the existence of solutions for vector equilibrium problems and vector equilibrium systems in cone b-metric spaces,and the Ekeland variational principle of vector form is proved by the method of partial order in vector space.With the help of this variational principle,we prove the existence of solutions for vector equilibrium problems and the existence of solutions for vector equilibrium systems in cone b-metric spaces.This paper is divided into three chapters.The first chapter is our introduction,we first introduce the historical background and development of Ekeland's variational principle,then we introduce the background and development of vector equilibrium problems and system of vector equilibrium problemsIn the second chapter,we study the existence of solutions for vector equilibrium in cone b-metric space.We introduce the partial order in cone b-metric space and prove Ekeland's variational principle by order method under certain conditions,and use the variational principle to show that the solution set of vector equilibrium problem is nonempty.The third chapter studies the existence of solutions for vector equilibrium systems in cone b-metric space.Based on the result of chapter,we prove the existence of solution for vector equilibrium systems by using partial order method.