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研究生: 黃子紜
論文名稱: 在完備的廣義度量空間三個收縮型函數(ψ,φ,ø)的定點定理
指導教授: 陳啟銘
陳正忠
口試委員:
學位類別: 碩士
Master
系所名稱: 南大校區系所調整院務中心 - 應用數學系所
應用數學系所(English)
論文出版年: 2013
畢業學年度: 101
語文別: 中文
中文關鍵詞: 廣義度量空間週期點固定點完備性
外文關鍵詞: generalized metric spaces, periodic points, fixed points, complete
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  • 摘要
    本篇論文主要是探討在完備廣義度量空間三個收縮型函數並證明了週期點及固定點這種類型的收縮定理。


    Abstract
    In this article, we introduce the notion of(ψ,φ,ø)-contraction on generalized metric spaces and prove the periodic points and fixed points for this type of contraction.

    目 錄 Abstract……………………………………………1 1.Introduction and preliminaries……………1 2.Main results……………………………………4 3.References ……………………………………15

    References
    [1] A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl., 1(1), (2008) 45–48.
    [2] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen., 57, (2000) 31–37.
    [3] C.M. Chen, Common fixed point theorems in complete generalized metric spaces, J. Appl. Math, Volume 2012 Article ID 945915, 14 pages.
    [4] C.M. Chen and W.Y. Sun, Periodic points and fixed points for the weaker (ø,ψ)-contractive mappings in complete generalized metric spaces, J. Appl.Math, Volume 2012 Article ID 856974, 7 pages.
    [5] C.M. Chen and C.H. Chen, Periodic points for the weak contraction mappings in complete generalized metric spaces, Fixed Point Theory and Applications,2012:79 doi:10.1186/1687-1812-2012-79.
    [6] P. Das, A fixed point theorem on a class of generalized metric spaces, Korea J. Math. Sci., 9, (2002) 29–33.
    [7] I.M Erhan, E. Karapinar and T. SekuLic, Fixed points of (ψ,ø) contractions on rectangular metric spaces, Fixed Point Theory and Applications,2012:138 doi:10.1186/1687-1812-2012-138.
    [8] H. Lakzian and B. Samet, Fixed points for (ψ,φ) -weakly contractive mappings in generalized metric spaces, Appl. Math. Lett., 25 (2012) 902–906.
    [9] D. Mihet, On Kannan fixed point principle in generalized metric spaces, J.Nonlinear Sci. Appl., 2(2), (2009) 92–96.
    [10] B. Samet, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal.,26(3), (2009) 1265–1271.
    [11] B. Samet, Disscussion on: A fixed point theorem of Banach-Caccioppli type on a class of generalized metric spaces, Publ. Math. Debrecen., 76(4),(2010) 493–494.

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