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作者(中文):魏廷宇
作者(外文):Wei, Ting-Yu.
論文名稱(中文):在偏豪斯多夫度量空間上弱收縮函數之定點定理
論文名稱(外文):Fixed point theorems for weak contractions on partial Hausdorff metric spaces.
指導教授(中文):陳啟銘
指導教授(外文):Chen, Chi-Ming
口試委員(中文):陳啟銘
陳正忠
林英哲
學位類別:碩士
校院名稱:國立清華大學
系所名稱:應用數學系所
學號:210424214
出版年(民國):106
畢業學年度:105
語文別:英文
論文頁數:26
中文關鍵詞:梅勒基勒R函數多值映射豪斯多夫
外文關鍵詞:pointFixedHausdorffmetriccontractionspartial
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本篇論文是研究關於梅勒-基勒類型函數和R 函數,相對於度
量空間中的部分豪斯多夫度量,多值映射的兩個新的固定點
定理。我們推廣和改進了文獻中部分豪斯多夫度量的最近固
定點定理。
The purpose of this paper is to study two new fixed point theorems for multi-valued mappings concerning the Meir-Keeler type functions and Rfunctions with respect to the partial Hausdorff metric Hp in completepartial metric spaces.
Our results generalize and improve many recent fixed point theorems for the partial Hausdorff metric in the literature.
1. Title、Abstract ........................... 1
2. Introduction and Preliminaries. ........... 3
3. Fixed Point Theorem via the Meir-Keeler type
function. ................................. 8
4. Fixed Point Theorem via the R-function ...15
5. References .............................. 24
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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 application
aux ´equations int´egrales, Fund. Math. 3 (1922) 133–181.
[7] Chi-Ming Chen, Erdal Karapinar,Fixed point results for the α-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] W.-S. Du, On coincidence point and fixed point theorems for nonlinear
multivalued maps, Topology and Applications, 159(2012), 49–56.
[10] 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.
[11] E. Karapinar, Weak φ-contraction on partial metric spaces, Journal of
Computational Analysis and Applications, 16(6),(2012) vol. 14, no. 2, pp.
206–210.
[12] E. Karapinar, Generalizations of Caristi Kirks theorem on partial metric
spaces, Fixed Point Theory and Applications, vol. 2011, article 4, 2011.
[13] E. Karapinar, I.M. Erhan, Fixed point theorem for cyclic maps on partial
metric spaces, Appl. Math. Inf. Sci., 6 (2012), 239–244.
[14] 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.
[15] Meir, A, Keeler, E: A theorem on contraction mappings, J. Math. Anal.
Appl., 28 (1969), 326–329
[16] S. B. Nadler Multi-valued contraction mappings, Pacific J. Math., 30
(1969), 475–488.
[17] S. Oltra, O. Valero, Banach’s fixed point theorem for partial metric spaces,
Rend. Istid Math. Univ. Trieste, 36 (2004) 17–26.
[18] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ-contractive
type mappings, Nonlinear Analysis, 75 (2012) 2154–2165.
[19] S. Reich, Fixed points of contractive functions, Boll Un Mat Ital., 75 (1972)
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