本論文的目的是研究在一個廣義平衡問題(簡稱，GEP)以及在一個希爾伯特空間內的非擴張映射的固定點問題裡，找到一般元素解的集合。首先，透過使用著名的KKM技術，我們為GEP得到輔助問題的解的存在和唯一性。其次，因為這個結果和納德勒的定理，我們透過黏性近似方法實施一個反覆的迭代找到各種GEP解的集合和各種非擴張映射的固定點的集合的一般元素。

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in a Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the GEP. Second, on account of this result and Nadler's theorem, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping.

1. Introduction 7
2. Preliminaries 12
3. Auxiliary Problem and Iterative Scheme 16
4. Strong Convergence Theorems 26
5. References 37

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