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作者(中文):彭湘嵐
論文名稱(中文):在度量空間上滿足KKM性質之ϕ-可允許的梅厄-基勒收縮函數之定點定理
指導教授(中文):陳啟銘
李俊璋
學位類別:碩士
校院名稱:國立新竹教育大學
系所名稱:應用數學系碩士班
學號:10124202
出版年(民國):103
畢業學年度:102
語文別:中文
論文頁數:18
中文關鍵詞:定點定理ϕ-可允許梅厄-基勒型式之集收縮KKM性質度量空間
外文關鍵詞:fixed pointϕ-admissible Meir-Keeler-type set contractionKKM propertyMetric space
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在這個碩士論文中,我們在完備度量空間上討論滿足KKM性質的ϕ-可允許梅厄-基勒型式之集收縮函數之定點定理。我們的結論推廣且改善最近的定點結果。
The purpose of this thesis is to study fixed point theorems for the KKM family satisfying the ϕ-admissible Meir-Keeler-type set contractions and ϕ-admissible weaker ψ-Meir-Keeler-type set contractions with respect to the measure of noncompactness α:B(M)→R^+ on complete metric spaces.Our results generalize and improve many recent fixed point results
in the literature.
Abrstract
1. Introduction and Preliminaries
2. Fixed point results for ϕ-admissible Meir-Keelertype set
contractions
3. Fixed point results for ϕ-admissible weaker ψ-Meir-Keeler-
type set contractions
References
[1] A. Amini, M. Fakhar, J. Zafarni, KKM mappings in metric spaces, Nonlinear Anal., 60, 1045–1052(2005).
[2] C.M Chen, KKM property and fixed point theorems in metric spaces, J. Math. Anal. Appl., 323, 323, 1231-V1237 (2006).
[3] C.M Chen, Fixed point theorems for a k-set contraction in a metric space, Applied Math. Letters 22, 101–104(2009) .
[4] C.M Chen, Tong-Huei Chang, Yueh-Hung Huang Approximate fixed point theorems for the generalized Ψ-set contraction mappings on an almost Φ-space, Applied Math. Letters 23, 152–155(2010) .
[5] C.M Chen, Tong-Huei Chang, Some results for the family 2g KKM(X, Y) and the "Φ" -mapping in hyperconvex metric spaces, Nonlinear Analysis 2533V2540 69, 2533–2540(2008)
[6] C.M Chen, Tong-Huei Chang, Fixed Point Theorems for a Weaker Meir-Keeler Type ψ-Set Contraction in Metric Spaces, Fixed Point Theory and Applications, Volume 2009, Article ID 129124, 8 pages doi:10.1155/2009/129124.
[7] Ky Fan, A generalization of Tychonoffs fixed point theorem, Math. Ann., 142, 305–310(1961).
[8] B. Knaster, C. Kuratowski, S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale Simplexe, Fund. Math., 14, 132–137(1929).
[9] Meir, A, Keeler, E: A theorem on contraction mappings. J. Math. Anal. Appl., 28, 326–329 (1969).
[10] M.A. Khamsi, N. Hussain, KKM mappings in metric type spaces. Nonlinear Anal., 73, 3123-V3129 (2010).
[11] R. Nussbaum, The fixed point index and fixed point theorems for k-set contractions, Doctoral Dissertation, University of Chicago, 1969.
[12] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis, 75 (2012) 2154–2165.
 
 
 
 
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