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研究生:李榮陞
研究生(外文):Li rung sheng
論文名稱:多值函數之選取
論文名稱(外文):Selections for Metric Projection
指導教授:楊南屏楊南屏引用關係
學位類別:碩士
校院名稱:輔仁大學
系所名稱:數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:19
中文關鍵詞:多值函數選取
外文關鍵詞:Selections
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  • 點閱點閱:185
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  • 下載下載:7
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文中,我們首先證明 ''Metric projection is a piecewise
polyhedral multifunction'',再以multifunction的觀點下,證明''continuous
extremal point selections''以及''quasi-linear selections''的存在定理,
最後,我們運用上述二存在定理,來證明在Metric projection的觀點下,
''continuous extremal point selections''以及''quasi-linear selections''
的存在定理。並試著找出''continuous extremal point and quasi-linear selections''
的存在定理。
We consider a metric projection as a piecewise polyhedral
multifunction. To see selections of metric projections, we first prove
the existence of continuous extremal point selections of piecewise polyhedral
multifunctions and quasi-linear selections of quasi-linear
multifunctions. The existence of selections to metric projections then
follows. Finally, we briefly explore the existence of continuous
quasi-linear extremal point selections of metric projections by an
example.
1 Introduction………………………………………………….. 1
2 Piecewise A_ne Functions and Metric Projections …………..3
3 Selections for Multifunctions…………………………………8
3.1 Continuous Extremal Point Selections………………...…8
3.2 Quasi-linear Selections………………………………….13
4 Selections of Metric Projections in (Rn; jj _ jj1)……………. 15
4.1 Continuous Extremal Point Selections of _K;1 ………….15
4.2 Quasi-linear Selections of _G;1 ………………………….16
References ……………………………………………………..19
[1] F. Deutsch, A survey of metric selections, in: Fixed Points and Nonexpansive
Mappings, ed. by R. C. Sine, Contemporary Mathematics, 18 (1983), 49-71.
[2] F. Deutsch, Best Approximation in Inner Product Spaces, Speinger-Verlag, New
York, 2001.
[3] F. Deutsch, Linear selections for the metric projection, J. Funct, Anal, 49
(1982), 269-292.
[4] M. Finzel, Linear approximation in l1
n , J. Approx. Theory, 76 (1994), 326-350.
[5] M. Finzel and W. Li, Piecewise a_ne selections for piecewise polyhedral mul-
tifunctions and metric projections, Journal of Convex Analysis, Vol.7, No.1
(2000), 73-94
[6] M. Gowda, M. Sznajder, Nondegeneracy concepts for zeros of piecewise smooth
functions, Math. Oper. Res. 23 (1998), 221-318.
[7] M. Gowda, M. Sznajder, On the pseudo-Lipschitzian behavior of the inverse of
a piecewise a_ne function, Math. Programming, 74, Ser. A (1996), 267-278.
[8] L. Kuntz, S. Scholtes, Structural analysis of nonsmooth mappings, inverse func-
tions, and metric projections, J. Math. Anal. Appl, 188 (1994), 346-384
[9] E. Michael, Continuous selections I, Annals of Math., 63 (1956), 361-382.
[10] G. Nurnberger, Schnitte fur die metrische Projektion, J. Approx. Theory, 20
(1977), 196-219.
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