Several Iterative Methods And Strong Convergence Theorems For Equilibrium Problems

Equilibrium problems provide us with a systematic framework to study a wide class of problems arising in finance economics, optimization and operation research etc.. In recent years, equilibrium problems have been deeply and thoroughly researched. See, for example, [1-3],[5-8] and [30-34]. Inspired and motivated by their work, in this paper, we introduce several iterative methods and their corresponding convergence theorems for equilibrium problems. Our paper is divided into three chapters.The first chapter is the induction which is constituted by two parts. They introduce the recent work of the famous authors in this field and contain corresponding lemmas and definitions respectively.In chapter two, by changing the kind of mappings, we obtain strong convergence for equilibrium problems and relatively nonexpansive mapping, nonexpansive mapping, strictly pseudocontractive mapping, asymptotically nonexpansive mapping respectively.In the third chapter, we intrduce some new iterative methods under the generalized projection and proof the strong convergence for these methods. As application, we obtain convergence for nonexpansive mapping and convex feasibility problems.Our results are new and can be viewed as generalizations and extensions of the corresponding results obtained in [14], [15], [24] and [28]. We also get the convergence property of the problems discussed in the papers [13]-[15], [21] and [22] etc. under mild conditions.In this paper, we also provide some new estimation techniques in the proofs of the results.