研究生: |
彭立成 |
---|---|
論文名稱: |
在偏豪斯多夫度量空間上滿足梅厄-基勒收縮函數之一些新定點理論 |
指導教授: | 陳啟銘 |
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: | 2016 |
畢業學年度: | 104 |
語文別: | 中文 |
中文關鍵詞: | 偏度量 、豪斯多夫 、梅厄-基勒 |
外文關鍵詞: | partial metric, Hausdorff, Meir-Keeler |
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 |
本文的目的是研究定點定理與在偏豪斯多夫度量空間上滿足梅厄-基勒收縮函數。我們的研究結果推廣和改進了最近許多固定點定理在局部Hausdorff度量上。
The purpose of this paper is to study fixed point theorems for a multivalued mapping concerning with three classes of Meir-Keeler contractions with respect to the partial Hausdorff metric H in complete partial metric spaces.
Our results generalize and improve many recent fixed point
theorems for the partial Hausdorff metric in the literature.
[1] T. Abdeljawad, Fixed points for generalized weakly contractive mappings
in partial metric spaces, Mathematical and Computer Modelling, 54(2011),
2923–2927.
[2] R.P. Agarwal, M.A. Alghamdi, N. Shahzad, Fixed point theory for cyclic
generalized contractions in partial metric spaces, Fixed Point Theory and
Appl., (2012), 2012.40.
[3] I. Altun, A. Erduran, Fixed point theorems for monotone mappings on
partial metric spaces, Fixed Point Theory and Appl., (2011), Article ID
508730, 10 pages, 2011.
[4] H. Aydi, Fixed point results for weakly contractive mappings in ordered
partial metric spaces, Journal of Advanced Mathematical Studies, 4(2011),
no. 2, pp. 1–12.
[5] H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler’s
fixed point theorem on partial metric spaces, Topology and Applications,
159(2012), 3234–3242.
[6] S. Banach, Sur les op´erations dans les ensembles abstraits et leur applica-
tion aux ´equations int´egrales, Fund. Math. 3 (1922) 133–181.
[7] Chi-Ming Chen, Erdal Karapinar,Fixed point results for the -Meir-Keeler
contraction on partialHausdorff metric spaces, Journal of Inequalities and
Applications 2013, 2013:410.
[8] K. P. Chi, E. Karapinar, T. D. Thanh, A generalized contraction principle
in partial metric spaces, Mathematical and Computer Modelling, 55(2012),
1673–1681.
[9] R.H. Haghi, Sh. Rezapour, N. Shahzad, Be careful on partial metric fixed
point results, Topology and its Applications,160(2013),no:3, 450–454.
[10] E. Karapinar, Weak -contraction on partial metric spaces, Journal of
Computational Analysis and Applications, 16(6),(2012) vol. 14, no. 2, pp.
206–210.
[11] E. Karapinar, Generalizations of Caristi Kirks theorem on partial metric
spaces, Fixed Point Theory and Applications, vol. 2011, article 4, 2011.
[12] E. Karapinar, I.M. Erhan, Fixed point theorem for cyclic maps on partial
metric spaces, Appl. Math. Inf. Sci., 6 (2012), 239–244.
[13] S.G. Matthews, Partial metric topology, Proc. 8th Summer of Conference
on General Topology and Applications, Ann. New York Aced. Sci., 728
(1994) 183–197.
[14] Meir, A, Keeler, E: A theorem on contraction mappings, J. Math. Anal.
Appl., 28 (1969), 326–329
[15] S. B. Nadler Multi-valued contraction mappings, Pacific J. Math., 30
(1969), 475–488.
[16] S. Oltra, O. Valero, Banach’s fixed point theorem for partial metric spaces,
Rend. Istid Math. Univ. Trieste, 36 (2004) 17–26.
[17] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for - -contractive
type mappings, Nonlinear Analysis, 75 (2012) 2154–2165.
[18] S. Reich, Fixed points of contractive functions, Boll Un Mat Ital., 75 (1972)
5(4):26–42.
22