臺灣博碩士論文加值系統

在這篇文章中，我們首先在Hilbert space下討論針對asymptotic nonspreading mapping 的固定點問題及系統廣義平衡點問題的共同解的強收斂定理。在應用部分，我們則是研究在系統平衡點問題和針對asymptotic nonspreading mapping 的固定點問題限制下的數學規劃問題，以及在系統最佳化問題和針對asymptotic nonspreading mapping 的固定點問題限制下的數學規劃問題解的收斂定理。

In this paper, we prove strong convergence theorems for finding a common element for the set of fixed points of asymptotic nonspreading mapping and the set of solutions of systems of generalized equilibrium problems in Hilbert spaces. As applications, we study the strong convergence theorems of finding the solution of mathematical program with a system of equilibrium constraints and fixed points of asymptotic nonspreading mappings, and solutions of a system of optimization problems and fixed points of asymptotic nonspreading mappings.

Contents
1 Introduction 1
2 Preliminaries 8
3 Main Results 10
4 Applications 26
5 References 30

1. F. Kohsaka, and W. Takahashi, Fixed point theorem for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math., 91 (2008), 166-177.
2. L. J. Lin, C. S. Chuang, and Z. T. Yu, Fixed points theorems for some new nonlinear mappings in Hilbert spaces, submitted.
3. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.
4. A. Genel, and J. Lindenstrass, An example concerning xed points, Israel. J. Math., 22 (1975), 81-86.
5. A. Tada, and W. Takahashi,Weak and strong convergence theorems for a non-expansive mappings and an equilibrium problem, J. Optim. Theory Appl., 133 (2007), 359-370.
6. P. Kumam, A hybrid approximation method for equilibrium and xed point problems for a monotone mapping and a nonexpansive mapping, Nonlinear Anal., 2 (2008), 1245-1255.
7. W. Takahashi, Y. Takeuchi, and R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 341 (2008), 276-286.
8. X. L. Qin, L. J. Lin, and S. M. Kang, On a generalized Ky Fan inequality and asymptotically strict pseudocontractions in the intermediate sense, J. Optim.
Theory Appl., doi:10.1007/s10957-011-9853-z.
9. W. Takahashi, Introduction to Nonlinear and Convex Analysis, Yokohoma Publishers, Yokohoma, 2009.
10. S. Itoh, and W. Takahashi, The common xed point theory of single-valued mappings and multi-valued mappings, Pacic J. Math., 79 (1978), 493-508.
11. W. Takahashi, and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428.
12. W. Takahashi, Nonlinear Functional Analysis-Fixed Point theory and its Ap-plications, Yokohama Publishers, Yokohama, 2000.
13. E. Blum, and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), 123-145.
14. P. L. Combettes, and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6 (2005), 117-136.
15. K. Goebel, and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.