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研究生:魏玄宇
研究生(外文):WEI, HSUAN-YU
論文名稱:對於新Meir-Keeler型條件的固定點定理之研究
論文名稱(外文):The study of fixed point theorems for new Meir-Keeler type conditions
指導教授:杜威仕
指導教授(外文):Wei-Shih Du
口試委員:陳中川左太政
口試委員(外文):Chung-Chuan ChenTso, Taicheng
口試日期:2024-05-28
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:2024
畢業學年度:112
語文別:英文
論文頁數:23
外文關鍵詞:Banach contraction principleMeir-Keeler type conditionfixed point theoremmetric space
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本文的主要研究目的是得到一個對於廣義Meir-Keeler型條件的新固定點定理及其在固定點理論中的應用。本文所建立的新結果改進和推廣了相應文獻中的一些結果。
The main research purpose of this paper is to provide a new fixed point theorem for generalized Meir-Keeler type conditions and its applications in fixed point theory. These new results established in this paper improve and generalize some results in the corresponding literature.
謝詞
Abstract
Key words and phrases
Introduction1
Main results4
Reference19
[1] T. Abdeljwad, Meir-Keeler α-contractive fixed and common fixed point theorems, Fixed Point Theory and Applications, 2013, 19 (2013).
[2] H. Aydi and E. Karapinar, A Meir-Keeler common type fixed point theorem on partial metric spaces, Fixed Point Theory and Applications, 2012, 26 (2012).
[3] S. Banach, Sur les op´erations dans les ensembles abstraits et leurs applications aux ´equations int´egrales, Fundamenta Mathematicae 3 (1922) 133-181.
[4] S.K. Chatterjea, Fixed-point theorems, Comptes Rendus de l’Academie bulgare des Sciences 25 (1972) 727-730.
[5] W.-S. Du, New simultaneous generalizations of common fixed point theorems of Kannan type, Chatterjea type and Mizoguchi-Takahashi type, Applied Mathematical Sciences 11(20) (2017) 995-1005.
[6] W.-S. Du, E. Karapinar, Z. He, Some simultaneous generalizations of wellknown fixed point theorems and their applications to fixed point theory, Mathematics 2018 6(7) 117.
[7] W.-S. Du, T.M. Rassias, Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications, International Journal of Nonlinear Analysis and Applications 11(1) (2020) 55-66.
[8] K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
[9] D.H. Hyers, G. Isac and Th. M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific Publ. Co., Singapore, New Jersey , London, 1997.
[10] Z. Kadelburg, S. Radenovic, Meir-Keeler-type conditions in abstract metric spaces, Applied Mathematics Letters 24(8) (2011) 1411-1414.
[11] Z. Kadelburg, R. Stojan, S. Shukla, Boyd-Wong and Meir-Keeler type theorems in generalized metric spaces, Journal of Advanced Mathematical Studies 9(1) (2016) 83-93.
[12] R. Kannan, Some results on fixed point–II, The American Mathematical Monthly 76 (1969) 405-408.
[13] S. Kanwal, A. Azam, Common fixed points of intuitionistic fuzzy maps for MeirKeeler type contractions, Advances in Fuzzy Systems, vol. 2018, Article ID 1989423, 6 pages, 2018.
[14] E. Karapınar, A. Rold´ an, J. Mart´ ınez-Moreno, C. Rold´ an, Meir-Keeler type multidimensional fixed point theorems in partially ordered metric spaces, Abstract and Applied Analysis, vol. 2013, Article ID 406026, 9 pages, 2013.
[15] M.A. Khamsi, W.A. Kirk, An introduction to metric spaces and fixed point theory, Pure and Applied Mathematics, Wiley-Interscience, New York, 2001.
[16] W.A. Kirk, N. Shahzad, Fixed point theory in distance spaces, Springer, Cham, 2014.
[17] T.C, Lim, On characterizations of Meir-Keeler contractive maps, Nonlinear Analysis, Theory, Methods and Applications 46(1) (2001) 113-120.
[18] A. Meir, E. Keeler, A theorem on contraction mappings, Journal of Mathematical Analysis and Applications 28(2) (1969) 326–329.
[19] Z. Mitrovic, S. Radenovic, On Meir-Keeler contraction in Branciari bmetric spaces, Transactions of A. Razmadze Mathematical Institute 173 (2019) 83-90.
[20] L. Pasicki, Meir and Keeler were right, Topology and its Applications 228 (2017) 382-390.
[21] V. Popa, A.M. Patriciu, A general fixed point theorem of Meir-Keeler type for mappings satisfying an implicit relation in partial metric spaces, Functional Analysis, Approximation and Computation 9(1) (2017) 53-60.
[22] E. Pourhadi, R. Saadati, and Z. Kadelburg, Some Krasnosel’skii-type fixed point theorems for Meir-Keeler-type mappings, Nonlinear Analysis : Modelling and Control 25(2) (2020) 257–265.
[23] S. Reich, A.J. Zaslavski, Genericity in nonlinear analysis, Springer, New York, 2014.
[24] Y. Rohen, T. Dosenovic, and S. Radenovic, A note on the paper a fixed point theorems in Sb-metric spaces, Filomat 31(11) (2017) 3335–3346.
[25] T. Senapati, L.K. Dey, B.A. Damjanovi´ c, New fixed results in orthogonal metric spaces with an application, Kragujevac Journal of Mathematics 42 (2018) 505–516.
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