Dissertation > Excellent graduate degree dissertation topics show

Several Iterative methods and Strong Convergence Theorems for Equilibrium Problems

Author: LiuBaoQing
Tutor: ZhangCongJun
School: Nanjing University of Finance and Economics
Course: Applied Mathematics
Keywords: Equilibrium problem nonexpansive mapping strictly pseudocontractive mapping convergence theorem
CLC: O177.2
Type: Master's thesis
Year: 2010
Downloads: 3
Quote: 0
Read: Download Dissertation

Abstract


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.

Related Dissertations

  1. The Existence of Positive Solutions of a Class of Fourth-order Nonlinear Differential Equations,O175
  2. Strong Convergence Theorems for Variational Inequalities Problem and Some Relative Researches,O178
  3. Bring Lower Bounds for Equilibrium Problems Existence of Solutions Xing , stability analysis and Its Algorithm,O177
  4. Viscosity Approximation Methods for Nonexpansive Mappings of Banach Space,O177.2
  5. Iterative Approximations of Fixed Points in Banach Spaces,O177.91
  6. Study on Vector Equilibrium Problems,O177
  7. Iterative Methods to the Common Elements of Equilibrium Problems and the Set of Fixed Points,O177.91
  8. The Strong Convergence of Iterations for Nonexpansive Nonself Mappings,O177.2
  9. Some Problems on Fixed Point Theory,O177.91
  10. Study on the Theory of Fixed Points in β-normed Linear Space,O177.91
  11. The Theorems on Existence of Fixed Point and Its Strong Convergence for Nonlinear Operator,O177.91
  12. Stability of Solutions for Vector Equilibrium Problems,O189.11
  13. Convergence of the Common Solution of Quasi-nonexpansive Mapping and Equilibrium Problem,O177.91
  14. Iterative Solutions of Variational Inclusions and Its Application,O177.91
  15. Sample Average Approximation Methods for Solving Stochastic Mixed Complementarity Problems,O221
  16. Predictor-corrector Methods for Solving Equilibrium Problems,O224
  17. Iterative Approximation of Fixed Points of Nonself-Asymptotically Purturbed Nonexpansive Mappings and Generalized Mixed Equilibrium Problems,O177.91
  18. Iterative Approximation Problems of Fixed Points for Nonlinear Operators,O177.91
  19. The Study of Correlated Problems of Solutions to Nonlinear Variational Inclusions,O177.91
  20. Algorithm Study for a Kind of the Variational Inequality Problem and the Split Feasibility Problem,O221

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Banach spaces and their linear operator theory.
© 2012 www.DissertationTopic.Net  Mobile