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Best periodic proximity points for cyclic weaker Meir-Keeler contractions. (English) Zbl 1245.49007
Summary: The purpose of this paper is to present the existence of the best period proximity point for cyclic weaker Meir-Keeler contractions and asymptotic cyclic weaker Meir-Keeler contractions in metric spaces.

49J27Optimal control problems in abstract spaces (existence)
47H09Mappings defined by “shrinking” properties
Full Text: DOI
[1] A. A. Eldred, W. A. Kirk, and P. Veeramani, “Proximal normal structure and relatively nonexpansive mappings,” Studia Mathematica, vol. 171, no. 3, pp. 283-293, 2005. · Zbl 1078.47013 · doi:10.4064/sm171-3-5
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[6] S. Karpagam and S. Agrawal, “Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps,” Nonlinear Analysis, vol. 74, no. 4, pp. 1040-1046, 2011. · Zbl 1206.54047 · doi:10.1016/j.na.2010.07.026
[7] W. A. Kirk, P. S. Srinivasan, and P. Veeramani, “Fixed points for mappings satisfying cyclical contractive conditions,” Fixed Point Theory, vol. 4, no. 1, pp. 79-89, 2003. · Zbl 1052.54032
[8] 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. · Zbl 1194.54059 · doi:10.1155/2010/572057 · eudml:228158
[9] S. L. Singh, S. N. Mishra, and R. Pant, “Fixed points of generalized asymptotic contractions,” Fixed Point Theory, vol. 12, no. 2, pp. 475-484, 2011. · Zbl 1241.54039
[10] C. Vetro, “Best proximity points: convergence and existence theorems for p-cyclic mappings,” Nonlinear Analysis, vol. 73, no. 7, pp. 2283-2291, 2010. · Zbl 1229.54066 · doi:10.1016/j.na.2010.06.008