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研究生:葉媺芳
研究生(外文):YEH, MEI-FANG
論文名稱:複雜非線性映射的新收斂定理
論文名稱(外文):New convergence theorems for complicated nonlinear mappings
指導教授:林英哲林英哲引用關係
指導教授(外文):Ing-Jer Lin
口試委員:杜威仕陳啟銘
口試日期:2021-08-02
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:26
中文關鍵詞:MT函數度量空間收斂定理循環映射最佳鄰近點
外文關鍵詞:MT -function (R-function)metric spaceconvergence theoremcyclic mappingbest proximity point
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設 U 和 V 是度量空間 (M,d) 和 G 的非空子集,U 是一個循環
映射。在本文中,我們將建立滿足以下條件的收斂定理。
因有特殊字元無法在網頁上精準呈現,請參閱全文檔說明。
Let U and V be nonempty subsets of a metric space (M, d) and G : U ∪ V → U ∪ V be a cyclic
mapping. In this paper, we will establish convergence theorems satisfying the following condition:

(C) there exists an MT -funtion κ : [0, ∞) → [0, 1) such that
d(Ga, Gb) ≤ κ (d (a, b)) maxd(a, b),[d(a, b) + d(b, Gb)],[d(a, Ga) + d(a, Gb) +d(b, Ga)] ,[d(a, Ga) + 2d(b, Gb)]
 ,[2d(a, b) + d(a, Gb) + d(a, Ga)],[3d(a, b) + d(a, Gb) +d(b, Ga)] + (1 − κ (d (a, b))) dist(U, V )for all a ∈ U and b ∈ V
因有特殊字元無法在網頁上精準呈現,請參閱全文檔說明。
 
1. Introduction and preliminaries 1
2. Some new convergence theorems 5
3. Reference 23
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Keeler type mappings in partially ordered metric spaces, Fixed Point Theory A., 2015 (2015)
1-16.
[2] S.S. Basha, Best proximity point theorems: An exploration of a common solution to ap-
proximation and optimization problems, Applied Mathematics and Computation 218 (2012)
9773-9780.
[3] S.S. Basha, N. Shahzed, R. Jeyaraj, Best proxmity point theorems: exposition of a signicant
non-linear porgramming porblem, Journal of Optimization Theory and Applications 56 (2013)
1699-1705.
[4] N. Bilgili, E. Karapinar, K. Sadarangani, A generalization for the best proximity point of
Geraghty-contractions, Journal of Inequalities and Applications 2013, 2013:286.
[5] W.-S. Du, On coincidence point and xed point theorems for nonlinear multivalued maps,
Topology and its Applications 159 (2012) 49-56.
[6] W.-S. Du, H. Lakzian, Nonlinear conditions for the existence of best proximity points, Journal
of Inequalities and Applications, 2012, 2012:206 doi:10.1186/1029-242X-2012-206.
[7] W.-S. Du, E. Karapinar, A note on Caristi-type cyclic maps: related results and applications,
Fixed Point Theory and Applications 2013, 2013:344.
[8] W.-S. Du, Y.-L. Liu, New nonlinear conditions for approximate sequences and new best prox-
imity point theorems, Applied Mathematical Sciences 11(49) (2017) 2447-2457.
[9] W.-S. Du, M.-C. Yen, New best proximity point theorems for a pair of nonlinear non-self
mappings in metric spaces, Nonlinear Analysis and Dierential Equations 5(6) (2017) 261-270.


[10] A.A. Eldered, P. Veeramani, Convergence and existence for best proximity points, Journal of
Mathematical Analysis Applications 323 (2006) 1001-1006.
[11] H. Lakzian, I.-J. Lin, Best proximity points for weak MT -cyclic Kannan contractions, Fun-
damental Journal of Mathematics and Applications, 1(1) (2018) 43-48.
[12] E. Karapinar, Best proximity points of cyclic mappings, Applied Mathematics Letters 25 (2012)
1761-1766.
[13] W.A. Kirk, P. S. Srinavasan, P. Veeramani, Fixed points for mapping satisfying cyclical con-
tractive conditions, Fixed Point Theory 4 (2003) 79-89.
[14] I.-J. Lin, H. Lakzian, Y. Chou, On best proximity point theorems for new cyclic maps, Inter-
national Mathematical Forum 7(37) (2012) 1839-1849.
[15] I.-J. Lin, H. Lakzian, Y. Chou, On convergence theorems for nonlinear mappings satisfying
MT -C conditions, Applied Mathematical Sciences, 6(67) (2012) 3329-3337.
[16] I.-J. Lin, Y.-L. Chang, Some new generalizations of Karapinar's theorems, International Jour-
nal of Mathematic Analysis 8 (2014) 957-966.
[17] I.-J. Lin, W.-S. Du, Y.-W. Wu, C.-H. Hsu, The existence of best proximity points and xed
points for new nonlinear mappings on quasiordered metric spaces, Bangmod International
Journal of Mathematical & Computational Science 1(1)(2015) 112-121.
[18] I.-J. Lin, C.-H. Chang, The study of generalizations of Lin-Chang's convergence theorems,
International Journal of Mathematical Analysis 9(54) (2015) 2649 - 2658.
[19] I.-J. Lin, Y.-J. Lin, S.-D. Hou, Some new best proximity point theorems and convergence
theorems for MT -functions, Nonlinear Analysis and Dierential Equations 4(4) (2016) 189 -198.


[20] I.-J. Lin, Y.-W. Wu, Some new convergence theorems for new nonlinear cyclic mappings on
metric spaces, Nonlinear Analysis and Dierential Equations 5(5) (2017) 217-227.
[21] I.-J. Lin, Y.-C. Cheng, Some new convergence theorems under nonlinear conditions on metric
spaces, International Mathematical Forum 13(5) (2018) 233 - 250.
[22] I.-J. Lin, W.-T. Chou, The study of convergence theorems for nonlinear cyclic mappings,
Nonlinear Analysis and Dierential Equations 6(1) (2018) 1-14.
[23] C. Mongkolkeha, Y. J. Cho, P. Kumam, Best proximity points for generalized proximal C-
contraction mappings in metric spaces with partial orders, J. Inequal. Appl. 2013 (2013), 12
[24] B. Zlatanov, A variational principle and coupled fixed points, Journal of Fixed Point Theory
and Applications 21 (2019) 1-13
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