臺灣博碩士論文加值系統

我們介紹在完備空間中的弱(Φ,ϕ)收縮函數，並在這類型的收縮下證明其週期點和固定點，我們的結果可推廣或改善最近許多文獻中的固定點定理

We introduce the notion of weaker (Φ,ϕ)-contractive mapping in completemetric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature

1.Introduction and Preliminaries
2.Main Results
3.Acknowledgment
4.References

[1] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations
integerales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922.
[2] D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical
Society, vol. 20, pp. 458–464, 1969.
[3] A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric
spaces,” Publicationes Mathematicae Debrecen, vol. 57, no. 1-2, pp. 31–37, 2000.
[4] A. Azam and M. Arshad, “Kannan fixed point theorem on generalized metric spaces,” Journal of
Nonlinear Sciences and Its Applications, vol. 1, no. 1, pp. 45–48, 2008.
[5] P. Das, “A fixed point theorem on a class of generalized metric spaces,” Journal of the Korean
Mathematical Society, vol. 9, pp. 29–33, 2002.
[6] D. Mihet¸, “On Kannan fixed point principle in generalized metric spaces,” Journal of Nonlinear Science
and Its Applications, vol. 2, no. 2, pp. 92–96, 2009.
[7] B. Samet, “A fixed point theorem in a generalized metric space for mappings satisfying a contractive
condition of integral type,” International Journal of Mathematical Analysis, vol. 3, no. 25–28, pp. 1265–
1271, 2009.
[8] B. Samet, “Discussion on “A fixed point theorem of Banach-Caccioppoli type on a class of generalized
metric spaces”,” Publicationes Mathematicae Debrecen, vol. 76, no. 3-4, pp. 493–494, 2010.
[9] H. Lakzian and B. Samet, “Fixed points for φ, ϕ-weakly contractive mappings in generalized metric
spaces,” Applied Mathematics Letters. In press.
[10] A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and
Applications, vol. 28, pp. 326–329, 1969.
[11] A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of
Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006.
[12] M. De la Sen, “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan
self-mappings,” Fixed Point Theory and Applications, vol. 2010, Article ID 572057, 23 pages, 2010.