迭代法被廣泛地應用在解決理論及應用科學中產生的線性及非線性問題，特別是在固定點理論和最佳化理論上。使用迭代法來尋找算子的固定點或最佳化問題的最佳解時，經由迭代會產生出一個序列。我們希望此序列能收斂至所探討之問題的解。因此，我們很自然的要求經由每次迭代產生的序列和問題的解集合之間的距離能逐次遞減。這也就是費葉爾單調性的本質想法。於本篇論文裡，我們研究擬費葉爾單調序列，即在費葉爾單調序列加上誤差。我們探討擬費葉爾單調序列的性質，特別舉例說明第I 型與第II 型擬費葉爾單調性之間互不隱含之關係。我們還討論了擬費葉爾序列的弱收斂性和強收斂性，包括對凸可行性問題之應用。

Iterative methods are extensively used to solve linear and nonlinear problems arising from both pure and applied sciences, and in particular, in fixed point theory and optimization. An iterative method which is used to find a fixed point of an operator or an optimal solution to an optimization problem generates a sequence in an iterative manner. We are in a hope that
this sequence can converge to a solution of the problem under investigation. It is therefore quite naturally to require that the distance of this sequence to the solution set of the problem under investigation be decreasing from iteration to iteration. This is the idea of Fejer-monotonicity. In this paper, We consider quasi-Fejer monotone sequences; that is, we consider Fejer monotone sequences together with errors. Properties of quasi-Fejer monotone sequences are investigated, weak and strong convergence of quasi-Fejer monotone sequences are obtained, and an application to the convex feasibility problem is included.

1 Introduction 1
2 Basic Properties of Quasi-fejer Sequences 4
2.1 Some Facts about Real Sequences 5
2.2 Basic Facts on Quasi-Fejer-monotonicity 6
2.3 Relationships of Quasi-Fejer-monotonicity of Types I and II 10
2.4 Subgradient Projections 14
2.5 A Characterization of Fejer-monotonicity 18
3 Weak and Strong Convergence of Quasi-fejer Sequences 20
4 Applications 25
References 32

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