臺灣博碩士論文加值系統

Let A and B be nonempty subsets of a metric space (X,d) and T:A∪B → A∪B be a cyclic mapping. In this paper, we establish some new convergence theorems
satisfying the following condition:
(G) there exists an MT-funtion ϕ:[0,∞) → [0,1) such that

d(Tx,Ty)≤ϕ(d(x,y))max{(1/4)[d(x,Ty)+2d(Tx,Ty)+d(y,Tx)],
(1/8)[d(x,Ty)+3d(x,Tx)+3d(y,Ty)+d(y,Tx)]}+[1-ϕ(d(x,y))]dist(A,B)
for all x∈A and y∈B.

1. Introduction and preliminaries 1
2. Some new convergence theorems in metric spaces 6
Reference 19

[1] M.A. Al-Thaga, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis: Theory, Methods and Applications 70 (2009)3665-3671.
[2] S.S. Basha, Best proximity point theorems: An exploration of a common solution to approximation 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 signicant 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] M. Derafshpour, Sh. Rezapour, N. Shahzad, On the existence of best proximity point of cyclic contractions, Advances in Dynamical Systems and Applications 6 (2011) 33-40.
[6] W.-S. Du, Some new results and generalizations in metric fixed point theory,Nonlinear Analysis: Theory, Methods and Applications 73 (2010) 1439-1446.
[7] W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology and its Applications 159 (2012) 49-56.
[8] W.-S. Du, New existence results of best proximity points and fixed points for MT(λ)-functions with applications to differential equations, Linear and Nonlinear Analysis 2(2) (2016) 199-213.
[9] W.-S. Du, Y.-L. Hung, A generalization of Mizoguchi-Takahashi's xed point
theorem and its applications to xed point theory, International Journal of Mathematical Analysis 11(4) (2017) 151-161.
[10] W.-S. Du, New xed point theorems for hybrid Kannan type mappings and MT(λ)-functions, Nonlinear Analysis and Differential Equations 5(2) (2017)
89-98.
[11] W.-S. Du, On hybrid Chatterjea type xed point theorem with MT(λ)-functions, Applied Mathematical Sciences 11(8) (2017) 397-406.
[12] W.-S. Du, On simultaneous generalizations of well-known fixed point theorems and others, International Journal of Mathematical Analysis 11(5) (2017) 225-232.
[13] W.-S. Du, Simultaneous generalizations of fixed point theorems of Mizoguchi-Takahashi type, Nadler type Banach type, Kannan type and Chatterjea type, Nonlinear Analysis and Dierential Equations 5(4) (2017) 171-180.
[14] W.-S. Du, New simultaneous generalizations of common xed point theorems of Kannan type, Chatterjea type and Mizoguchi-Takahashi type, Applied Mathematical Sciences 11(20) (2017) 995-1005.
[15] W.-S. Du, H. Lakzian, Nonlinear conditions for the existence of best proximity points, Journal of Inequalities and Applications, 2012, 2012:206.
[16] M. De La Sen, R.P. Agarwal, Common xed points and best porximity points of two cyclic self-mappings, Fixed Point Theory and Applications 2012, 2012:136.
[17] A.A. Eldered, P. Veeramani, Convergence and existence for best proximity points,Journal of Mathematical Analysis Applications 323 (2006) 1001-1006.
[18] E. Karapinar, Best proximity points of cyclic mappings, Applied Mathematics Letters 25 (2012) 1761-1766.
[19] W.A. Kirk, P. S. Srinavasan, P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory 4 (2003) 79-89.
[20] I.-J. Lin, H. Lakzian, Y. Chou, On best proximity point theorems for new cyclic maps, International Mathematical Forum 7(37) (2012) 1839-1849.
[21] 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.
[22] I.-J. Lin, Y.-L. Chang, Some new generalizations of Karapinar's theorems, International Journal of Mathematic Analysis 8 (2014) 957-966.
[23] 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.
[24] I.-J. Lin, Y.-J. Lin, S.-D. Hou, Some new best proximity point theorems and convergence theorems for MT-functions, Nonlinear Analysis and Differential Equations 4(4) (2016) 189-198.
[25] C. Mongkolkeha, P. Kuman, Best porximity point theorems for generalized cyclic contractions in ordered metric spaces, Journal of Optimization Theory and Applications 155 (2012) 215-226.
[26] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
[27] M. Pacurar, I.A. Rus, Fixed point theory for cyclic '-contractions, Nonlinear Analysis: Theory, Methods and Applications 72 (2010) 1181-1187.
[28] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136 (5) (2008) 1861-1869.
[29] T. Suzuki, M. Kikkawa, C. Vetro, The existence of the best proximity points in metric spaces with the property UC, Nonlinear Analysis: Theory, Methods and Applications 71 (2009) 2918-2926.
[30] V. Vetrivel, P. Veeramani, P. Bhattacharyya, Some extensions of Fan's best approximation theorem, Numerical Functional Analysis and Optimization 13(3-4) (1992) 397-402.