臺灣博碩士論文加值系統

此篇論文的目標是提出以黏質性方法
尋求在 Hilbert 空間 H 的閉凸子集C 上之有限多個非擴張映象T={ T_{i} }_{i=1}^{N}特定公共固定點。
我們提出兩種模式來解決這類問題：
其一為隱式,另外一個為顯式.。
隱式模式是透過固定點方程式
x_{t}= tf (x_{t} ) + (1− t)Tx_{t} ，
在 f :C →C為約縮映象下,
找到集合 {x_{t} : 0 < t < 1} 。
顯式模式是將隱式離散化，且藉由遞迴式
x_{n+1}=α\_{n}f(x_{n}) +(1−α\_{n})Tx_{n}，在 n ≥ 0，
{α\_{n} }⊂ (0,1) 下，
定義序列 {x_{n} }。
我們所提到的隱式模式和顯式模式兩者都範數收斂於 T 的固定點，
此部分已被文獻所證明.
(在顯式中強加了另外的條件於序列{α _{n} } )。
我們將在有限多個非擴張映象集合中延伸這兩種模式。我們另外也藉由所提到的模式其範數收斂到此集合的公共固定點去求解變分不等式。

The aim of this work is to propose viscosity-like methods for finding a specific common fixed point of a finite family T={ T_{i} }_{i=1}^{N} of nonexpansive self-mappings of a closed convex subset C of a Hilbert space H.We propose two schemes: one implicit and the other explicit.The implicit scheme determines a set {x_{t} : 0 < t < 1} through
the fixed point equation x_{t}= tf (x_{t} ) + (1− t)Tx_{t}, where f : C→C is a contraction.The explicit scheme is the discretization of the implicit scheme and de defines a sequence {x_{n} } by the recursion x_{n+1}=α\_{n}f(x_{n}) +(1−α\_{n})Tx_{n} for n ≥ 0, where {α\_{n} }⊂ (0,1) It has been shown in the literature that both implicit and explicit schemes converge in
norm to a fixed point of T (with additional conditions imposed on the sequence {α _{n} } in the explicit scheme).We will extend both schemes to the case of a finite family of nonexpansive mappings. Our proposed schemes converge in norm to a common fixed point of the family which in addition solves a variational inequality.

Abstract---------------------------------i
1 Introduction-------------------------1
2 Preliminaries-----------------------4
3 The Main Results------------------6
3.1 An Implicit Scheme-------------7
3.2 An Explicit Scheme-------------13
Reference------------------------------22

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