Equilibrium Problems With Lower And Upper Bounds: Existence Of Solutions, Stability Analysis And Algorithmic Aspect

point problems, complementarity problems, optimization, saddle point problems and Nash equilibrium problems as special cases. Equilibrium problems provide us with a systematic framework to study a wide class of problems arising in finance economics, optimization and operation research, etc., which motivate the extensive concern. In recent years, equilibrium problems have been deeply and thoroughly researched. In equilibrium problems, there exists a very interesting problem—equilibrium problems with lower and upper bounds, which is an open problem raised by Isac, Sehgal and Singh in 1999. As to this kind of equilibrium problems with lower and upper bounds, the solution existence and algorithm as well as the stability of solution sets have been studied more and more. Inspired and motivated by these research results, this paper is devoted to studying equilibrium problems with lower and upper bounds, the main work is as follows:Chapter 2 uses some classical fixed point theorems to derive the solution existence theorems of equilibrium problems with lower and upper bounds. Chapter 3 is devoted to investigating the stability of solution sets in a Hausdorff topological vector space, in the case where a set K and a mapping f are perturbed respectively by parametersλandμ. Then, we study the stability of solution sets in a vector metric space, in the particular case where K is fixed, and f is perturbed by a parameterε. In Chapter 4, solution algorithms are established by Viscosity approximation methods and three-order differential proximal methods, furthermore, we analyze the convergence of the algorithms.