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Chen, Chiming; Lin, Chingju

Best periodic proximity points for cyclic weaker Meir-Keeler contractions. (English) Zbl 1245.49007

J. Appl. Math. 2012, Article ID 782389, 7 p. (2012).
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.

Cited in 7 Documents

MSC:

49J27 Existence theories for problems in abstract spaces
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

uniformly convex Banach space; best period proximity point; cyclic weaker Meir-Keeler contractions; asymptotic cyclic weaker Meir-Keeler contractions
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\textit{C. Chen} and \textit{C. Lin}, J. Appl. Math. 2012, Article ID 782389, 7 p. (2012; Zbl 1245.49007)
Full Text: DOI

References:

[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
[2] 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. · Zbl 1105.54021
[3] A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326-329, 1969. · Zbl 0194.44904
[4] C. Di Bari, T. Suzuki, and C. Vetro, “Best proximity points for cyclic Meir-Keeler contractions,” Nonlinear Analysis, vol. 69, no. 11, pp. 3790-3794, 2008. · Zbl 1169.54021
[5] S. Sadiq Basha, “Best proximity point theorems,” Journal of Approximation Theory, vol. 163, no. 11, pp. 1772-1781, 2011. · Zbl 1229.54049
[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
[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
[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
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