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作者(中文):林政勳
論文名稱(中文):在完備準度量空間上循環弱梅厄-基勒φ-收縮映射之定點定理
指導教授(中文):陳正忠
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:10124201
出版年(民國):103
畢業學年度:102
語文別:中文
論文頁數:14
中文關鍵詞:度量空間收縮函數定點定理梅厄-基勒循環
外文關鍵詞:metric-like spacescontractive mappingFixed point theoryMeir-Keelercyclic
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在本文中,我們利用Meir-Keeler函數,可允許函數,循涵函數等概念,去介紹一新的循環弱Meir-Keeler可允許函數,並在此新函數上探討定點定理。
Fixed point theory for the cyclic weaker Meir-Keeler
φ-contractive mapping on complete metric-like spaces
目錄
Abrstract………………………………………………1
1.Introduction and Preliminaries……………2
2.Main results……………………………………6
3.References…………………………………………13
References:
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[3] Aage, CT, Salunke, JN: Some results of fixed point theorem in dislocated quasi-metric spaces. Bull. Marathwada Math. Soc. 9, 1-5 (2008)
[4] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for contractive
type mappings, Nonlinear Analysis, 75 (2012) 2154-2165.
[5] Chen, CM: Fixed point theorems for cyclic Meir-Keeler type mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 41 (2012)
[6] Daheriya, RD, Jain, R, Ughade, M: Some fixed point theorem for expansive type mapping in dislocated metric space, ISRN Math, Anal. 2012, Article ID 376832 (2012)
[7] Eldered, AA, Veeramani, P: Convergence and existence for best proximity points. J. Math. Anal. Appl. 323, 1001-1006 (2006)
[8] Eldered, AA, Veeramani, P: Proximal pointwise contraction. Topol. Appl. 156, 2942-2948 (2009)
[9] Hitzler, P: Generalized metrics and topology in logic programming semantics. PhD thesis, School of Mathematics, Applied Mathematics and Statistics, National University Ireland, University College Cork (2001)
[10] Hitzler, P, Seda, AK: Dislocated topologies. J. Electr. Eng. 51(12), 3-7 (2000)
[11] Kirk, WA, Srinavasan, PS, Veeramani, P: Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 4, 79-89 (2003) [7] Sarma, IR, Kumari, PS: On dislocated metric spaces. Int. J. Math. Arch. 3(1), 72-77 (2012)
[12] Karapınar, E: Fixed point theory for cyclic weak contraction. Appl. Math. Lett. 24, 822-825 (2011)
[13] Karapınar, E, Erhan, IM, Ulus, AY: Fixed point theorem for cyclic maps on partial metric spaces. Appl. Math. Inf. Sci. 6(1), 239-244 (2012)
[14] Karapınar, E, Sadarangani, K: Fixed point theory for cyclic ( ) contractions. Fixed Point Theory Appl. 2011, 69 (2011)
[15] Karpagam, S, Agrawal, S: Best proximity points theorems for cyclic Meir-Keeler contraction maps. Nonlinear Anal. 74, 1040-1046 (2011)
[16] Karpagam, S, Agrawal, S: Existence of best proximity points of p-cyclic contractions. Fixed Point Theory 13(1), 99-105 (2012)
[17] Matthews S. G., Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197.
[18] Meir, A, Keeler, E, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326–329, 1969
[19] Mongkolkeha, C, Kumam, P: Best proximity point theorems for generalized cyclic contractions in ordered metric spaces. J. Optim. Theory Appl. (2012). doi:10.1007/s10957-012-9991-y

[20] Nashine, HK, Sintunavarat, W, Kumam, P: Cyclic generalized contractions and fixed point results with applications to integral equation. Fixed Point Theory Appl. 2012, 217 (2012)
[21] P˘acurar, M, Rus, IA: Fixed point theory for cyclic ϕ-contractions. Nonlinear Anal. 72(3-4), 1181-1187 (2010)
[22] Petru,sel, G: Cyclic representations and periodic points. Stud. Univ. Babe,s-Bolyai, Math. 50, 107-112 (2005)
[23] Rezapour, S, Derafshpour,M, Shahzad, N: Best proximity point of cyclic ϕ-contractions in ordered metric spaces. Topol. Methods Nonlinear Anal. 37, 193-202 (2011)
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[25] Shrivastava, R, Ansari, ZK, Sharma, M: Some results on fixed points in dislocated and dislocated quasi-metric spaces. J. Adv. Stud. Topol. 3(1), 25-31 (2012)
[26] Sintunavarat, W, Kumam, P: Common fixed point theorem for cyclic generalized multi-valued contraction mappings. Appl. Math. Lett. 25(11), 1849-1855 (2012)
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