簡易檢索 / 詳目顯示

研究生: 吳姿慧
Tzi-Hui Wu
論文名稱: 在錐度量空間中的多值收縮之固定點定理
Fixed point theorems of the set-valued contractions in cone metric spaces
指導教授: 陳啟銘
Chi-Ming Chen
陳正忠
Jeng-Chung Chen
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: 2012
畢業學年度: 101
語文別: 英文
論文頁數: 12
中文關鍵詞: 固定點錐度量空間Meir-Keeler 錐型映射多值收縮
外文關鍵詞: Fixed point, Cone metric space, Meir-Keeler cone-type mapping, Set-valued contraction
相關次數: 點閱:3下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本篇論文主要是探討在錐度量空間上有關於stronger Meir-Keeler錐型映射的多值收縮之固定點。我們的結果推廣了最近的研究結果Kadelburg和Radenovi'c[26,27,33]和Wardowski[43]。


    The purpose of this paper is to present the fixed points of the set-valued contractions concerning with the stronger Meir-Keeler cone-type mappings in cone metric spcaes. Our results generalize the recent results of Kadelburg and Radenovi´c [26, 27, 33] and Wardowski [43].

    Abrstract 1.Introduction and Preliminaries 2.Main results 3.References

    [1] M. Abbas, G. Jungck, Common fixed point results for
    noncommuting mappings without continuity in cone
    uniform spaces, J. Math. Anal. Appl., 341(2008) No.1,
    416-420.
    [2] M. Alimohammady, J. Balooee, S. Radojevi´c, V.
    Rakoˇcevi´c, M. Roohi,Conditions of regularity in
    cone metric spaces, Appl. Math. Comput.,
    2011doi:10.1016/j.amc.2011.01.010 1.3.1.9.
    [3] A. Amini-Harandi, M. Fakhar, Fixed point theory in cone
    metric spaces obtained via the scalarization
    method,Comput. Math. Appl., 59 11 (2010),3529V3534.
    [4] M. Arshad, A. Azam, P. Vetro, Some common fixed point
    results in cone uniform spaces, Fixed Point Theory and
    Appl., 2009 Vol. 2009, Article ID 493965, 11 Pages,
    doi:10.1155/2009/493965.
    [5] M. Asadi, H. Soleimani, S. M. Vaezpour, An Order on
    Subsets of Cone Metric Spaces and Fixed Points of Set-
    Valued Contractions, Fixed Point Theory and
    Applications, 2009 Volume 2009, Article ID 723203,
    8 pages,doi: 10.1155/2009/723203.
    [6] A. Azam, M. Arshad, Common fixed points of generalized
    contractive maps in cone uniform spaces, Bull. Iranian
    Math. Soc., 35 (2) (2009) 255-264.
    [7] S. Banach, Sur les operations dans les ensembles
    abstraits et leur application aux equations
    integerales, Fund. Math., 3(1922), 133V181.
    [8] C.D. Bari, P. Vetro, '-pairs and common fixed points in
    cone metric spaces,Rend. Circ. Mat. Palermo,57(2002)
    No.2, 279-285.
    [9] C. Di Bari, P. Vetro, Weakly '-pairs and common fixed
    points in cone metric spaces, Rend. Circ. Mat.
    Palermo,58 (2009) 125-132.
    [10] C. Di Bari, T. Suzuki, C. Vetro, Best proximity for
    cyclic Meir-Keeler contractions, Nonlinear Anal.,69
    (2008) 3790-3794.
    [11] Cristina Di Bari, Reza Saadati, Pasquale Vetro, Common
    fixed points in cone metric spaces for CJM-pairs,
    Mathematical and Computer Modelling,2011
    doi: 101016/j.mcm.2011.05.043.
    [12] D.W. Boyd, J.S.W. Wong, On nonlinear contractions,
    Proc. Am. Math. Soc., 20(1969), 458V464.
    [13] S.K. Chatterjea, Fixed-point theorems, C. R. Acad.
    Bulgare Sci., 25(1972),727-730.
    [14] S.C. Chu, J.B. Diaz, Remarks on a generalization of
    Banach’s principle of contraction mappings, J. Math.
    Anal. Appl., 2(1965), 440V446.
    [15] Hui-Sheng Ding, Zoran Kadelburg, Erdal Karapinar,
    Stojan Radenovi´c,Common fixed points of weak
    contractions in cone metric spaces, Abstract and
    Applied Analysis, 2012 In Press.
    [16] M. Geraghty, On contractive mappings, Proc. Amer.
    Math. Soc.40(1973),604-608.
    [17] J. Harjani, K. Sadarangani, Generalized contractions
    in partially ordered metric spaces and applications to
    ordinary differential equations, Nonlinear Anal.,72
    (2010) 1188-1197.
    [18] R.H. Haghi, Sh. Rezapour, Fixed points of
    multifunctions on regular cone metric spaces, Expo.
    Math.,28(2010) 71-77.
    [19] X. Huang, C. Zhu, X. Wen A common fixed point theorem
    in cone metric spaces, Int. J. Math. Anal.4(2010),
    No.15, 721-726.
    [20] L. G. Huang, X. Zhang, Cone metric spaces and fixed
    point theorems of contractive mappings, J. Math. Anal.
    Appl.322(2007), 1468-1476.
    [21] S. Jankovi´c, Z. Kadelburg, S. Radonevi´c, On cone
    metric spaces: A survey,Nonlinear Anal.,2011 2591-2601.
    [22] S. Jankovi´c, Z. Kadelburg, S. Radonevi´c, B. E.
    Rhoades, Assad-Kirk-type Fixed point Theorems for a
    Pair of Nonself Mappings on Cone Metric Spaces, Fixed
    Point Theory and Applications,2009 Article ID 761086,
    16 pages, doi: 10.1155/2009/761086.
    [23] G. Jungck, S. Radenovi´c, S. Radojevi´c, and V.
    Rakoˇcevi´c, Common fixed point theorems for weakly
    compatible pairs on cone metric spaces, Fixed Point
    Theory and Applications,2009 Vol. 2009, Article ID
    643840, 13 pages,doi: 10.1155/2009/643840.
    [24] R. Kannan, Some results on fixed points, Bill.
    Calcutta Math. Soc.,60(1968), 71-76.
    [25] Z. Kadelburg, S. Radenovi´c, V. Rako´cevi´c, A note on
    the equivalence of some metric and cone metric fixed
    fixed point results, Appl. Math. Lett.,24(2011), 370-
    374.
    [26] Z. Kadelburg, S. Radenovi´c, Meir-Keeler-type
    conditions in abstract metric spaces, Appl. Math.
    Lett., 24(2011), 1411-1414.
    [27] Z. Kadelburg, S. Radenovi´c, Some results on set-
    valued contractions in abstract metric spaces,
    Computers and Mathematics with Applications.,62(2011),
    342-350.
    [28] D. Kilm, D. Wardowski, Dynamic processes and fixed
    points of set-valued nonlinear contractions in cone
    metric spaces, Nonlinear. Anal., 71(2009),5170-5175.
    [29] A. Meir, E. Keeler, A theorem on contraction mappings,
    J. Math. Anal.Appl. 28(1969), 326-329.
    [30] N. Mizoguchi, W. Takahashi, Fixed point theorems for
    multivalued mappingson complete metric spaces, J. Math.
    Anal. Appl., 141(1989), 177-188.
    [31] P. D. Proinov, A unified theory of cone metric spaces
    and its applications to the fixed point theory, ArXiv:
    111.4920, 2011, 51 pages.
    [32] S.B. Nadler Jr, Multi-valued contraction mappings,
    Pacific J. Math.,30(1969), 475-488.
    [33] S. Radenovi´c, Z. Kadelburg, Some results on fixed
    points of multifunctions on abstract metric spaces,
    Mathematical and Computer Modelling,53(2011), 746-754.
    [34] Sh. Rezapour, R. H. Haghi, N. Shahzad, Some Notes on
    fixed points of quasicontraction maps, Appl. Math.
    Lett., 23 (2010), 498-502.
    [35] Sh. Rezapour, H. Khandani, S. M. Vaezpour, Efficacy of
    Cones on Topological Vector Spaces and Application to
    Common Fixed Points of Multifunctions, Rend. Circ. Mat.
    Palermo, 59 (2010), 185-197.
    [36] Sh. Rezapour, R. H. Haghi, Fixed point of
    multifunctions on cone metric spaces, Numer. Funct.
    Anal. and Opt., 30 (7-8) (2009) 825-832.
    [37] Sh. Rezapour, M. Drafshpour, R. Hamlbarani, A review
    on topological properties of cone metric spaces,
    Analysis Topology and Appl., (2008)Vrnjacka Banja,
    Serbia, from May 30to June 4, 2008.
    [38] Sh. Rezapour, R. Hamlbarani, Some notes on the
    paper ”Cone metric spaces and fixed point theorems of
    contractive mappings”, J. Math. Anal.Appl., 345 (2008)
    719-724.
    [39] I.A. Rus, Generalized contractions and applications,
    Cluj Univ. Press, Cluj-Napoca, NO. 2(2001).
    [40] T. Suzuki, Fixed-point theorem for asymptotic
    contractions of Meir-Keeler type in complete metric
    spaces, Nonlinear Anal., 6464 (2006), 971-978.
    [41] T. Suzuki, Moudafis viscosity approximations with Meir-
    Keeler contractions, J. Math. Anal. Appl., 325(2007),
    342-352.
    [42] K. Wlodarczyk, R. Plebaniak, C. Obczynski, Convergence
    theorems, best approximation and best proximity for set-
    valued dynamic systems of relatively quasi-asyptotic
    contractions in cone uniform spaces, Nonlinear.Anal., 72
    (2009), 794-805.
    [43] D. Wardowski, Endpoints and fixed points of set-valued
    contractions in cone metric spaces, Nonlinear. Anal.,
    71(2009), 512-516.
    [44] P.P. Zabrejko, K-metric and K-normed linear spaces:
    survey, Collect.Math.,48 4-6(1997), 825-859.
    [45] Z. Zhao, X. Chen, Fixed points of decreasing operators
    in ordered Banach spaces and applications to nonlinear
    second order elliptic equations, Computer and Math.with
    Appl.,58(2009), 1223-1229.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE