研究生: |
鄭恬瀅 |
---|---|
論文名稱: |
廣義錐度量拓樸向量空間定理 A note on tvs-G-cone metric fixed point |
指導教授: |
陳啟銘
Chi-Ming 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: | 18 |
中文關鍵詞: | 固定點 、CBW函數 、Tvs-G錐度量空間 |
外文關鍵詞: | Fixed point, CBW function, ]tvs-G-cone metric space |
相關次數: | 點閱:1 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 |
在這篇論文中,探討在拓普向量錐度量空間上一些性質,並在此空間上討論一些性質和CBW函數的定點定理 。
In this paeper, for a tvs-G-cone metric space (X,G) and for the family
A of subsets of X, we introduce a new notion of the tvs-H-cone metric
H with respect to G, and we get a fixed result for the CBW-tvs-G-conetype-
function in a complete tvs-G-cone metric space (A,H). Our results
generalize some recent results in the literature.
[1] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems
of contractive mappings, J. Math. Anal. Appl., 322(2007), 1468-1476.
[2] M. Abbas and 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.
[3] S. Jankovic0 , Z. Kadelburg, S. Radonevic and B. E. Rhoades, Assad-Kirktype
fixed point theorems for a pair of nonself mappings on cone metric
spaces, Fixed Point Theory Appl.,2009 Vol. 2009, 16 pages, Article ID
761086, doi:10.1155/2009/761086.
[4] Sh. Rezapour and 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.
[5] M. Arshad, A. Azam and P. Vetro, Some common fixed point results in
cone uniform spaces, Fixed Point Theory Appl., 2009 Vol. 2009, Article ID
493965, 11 Pages, doi:10.1155/2009/493965.
[6] A. Azam and M. Arshad, Common fixed points of generalized contractive
maps in cone uniform spaces, Bull. Iranian Math. Soc., 35 (2) (2009) 255-
264.
[7] C.D. Bari and P. Vetro, '-pairs and common fixed points in cone metric
spaces, Rend. Circ. Mat. Palermo, 57(2002) No.2, 279-285.
[8] C. Di Bari and P. Vetro, Weakly '-pairs and common fixed points in cone
metric spaces, Rend. Circ. Mat. Palermo, 58 (2009) 125-132.
[9] J. Harjani and K. Sadarangani, Generalized contractions in partially ordered
metric spaces and applications to ordinary differential equations,
Nonlinear Anal., 72(2010) 1188-1197.
[10] R.H. Haghi and Sh. Rezapour, Fixed points of multifunctions on regular
cone metric spaces, Expo. Math., 28(2010) 71-77.
[11] D. Kilm and D. Wardowski, Dynamic processes and fixed points of
set-valued nonlinear contractions in cone metric spaces, Nonlinear.
Anal.,71(2009), 5170-5175.
[12] Z. Kadelburg, S. Radenovic0 , V. Rakoˇcevic0 , Remarks on ”quasi-contraction
on a cone metric space”, Appl. Math. Lett., 22 (2009), 1674-1679.
[13] Z. Kadelburg, M. Pavlovic0, S. Radenovic0 , Common fixed point theorems
for ordered contractions and quasi-contractions in ordered cone metric
spaces, Computer Math. Appl., (2010), doi:10.1016/j.camwa.2010.02.039.
[14] Sh. Rezapour, H. Khandani and 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.
[15] Sh. Rezapour and R. H. Haghi, Fixed point of multifunctions on cone metric
spaces, Numer. Funct. Anal. and Opt., 30 (7-8) (2009) 825-832.
[16] W.S. Du, A note on cone metric fixed point theory and its equivalence,
Nonlinear Analysis. Theory, Methods Applications, 72 (2010) 2259-2261.
[17] A. Azam, I. Beg and M. Arshad, Fixed point in topological vector spacevalued
cone metric spaces, Fixed Point Theory and Applications, 2010
(2010) doi:10.1155/2010/604084. Article ID 604084, 9 pages.
[18] I. Beg, A. Azam and M. Arshad, Common fixed points for maps on topological
vector space valued cone metric spaces, International Journal of
Mathematics and Mathematical Sciences, 2009, Article ID 560264, 8 pages.
[19] Z. Kadelburg, S. Radenovic0 and V. Rakoˇcevic0 , Topological vector space
valued cone metric spaces and fixed point theorems, Fixed Point Theory
and Applications, (2010) doi:10.1155/2010/170253. Article ID 170253, 17
pages.
[20] Z. Kadelburg, S. Radenovic0 and V. Rakoˇcevic0 , A note on equivalence
of some metric and cone metric fixed point results, Applied Math. Lett.,
24(2011) 370-374.
[21] B. C. Dhage,, Generalized metric space and mapping with fixed point, Bull.
Calcutta. Math. Soc., 84 (1992), 329-336.
[22] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J.
Nonlinear and Convex. Anal. 7(2006) No.2, 289-297.
[23] S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 5
(1972), 26-42.
[24] Stojan Radonevic0 , Suzana Simic0 , Nenad Cakic0 , Zorana Golubovic0, A
note on tvs-cone metric fixed point theory, Mathematical and Computer
Modelling, 54(2011), 2418-2422.
[25] Zoran Kadelburg, Stojan Radenovic0 , Coupled fixed point results under tvscone
metric and w-cone-distance, Advanced in Fixed Point Theory, 2(2012),
29-46.
[26] Lj. C0 iric0 , H. Lakzian, V. Rakoc0evic0 , Fixed point theorems for w-cone distance
contraction mappings in tvs-cone metric spaces, Fixed Point Theory
Appl., 2012:3 (2012),doi:10.1186/1687-1812-2012-3.