Best proximity point theorems for generalized cyclic contractions in ordered metric spaces. (English) Zbl 1257.54041
Summary: We generalize cyclic contractions on partially ordered complete metric spaces. We prove some fixed point theorems as well as some theorems on the existence of best proximity points. Our results improve and extend some recent results in previous work.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
References:
| [1] | Arvanitakis, A.D.: A proof of the generalized Banach contraction conjecture. Proc. Am. Math. Soc. 131, 3647–3656 (2003) · Zbl 1053.54047 · doi:10.1090/S0002-9939-03-06937-5 |
| [2] | Choudhury, B.S., Das, K.P.: A new contraction principle in Menger spaces. Acta Math. Sin. 24, 1379–1386 (2008) · Zbl 1155.54026 · doi:10.1007/s10114-007-6509-x |
| [3] | Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory Appl. 4, 79–89 (2003) · Zbl 1052.54032 |
| [4] | Eldred, A.A., Kirk, W.A., Veeramani, P.: Proximal normal structure and relatively nonexpansive mappings. Stud. Math. 171, 283–293 (2005) · Zbl 1078.47013 · doi:10.4064/sm171-3-5 |
| [5] | Eldred, A.A., Veeramani, P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323, 1001–1006 (2006) · Zbl 1105.54021 · doi:10.1016/j.jmaa.2005.10.081 |
| [6] | Suzuki, T., Kikkawa, M., Vetro, C.: The existence of best proximity points in metric spaces with the property UC. Nonlinear Anal. 71, 2918–2926 (2009) · Zbl 1178.54029 · doi:10.1016/j.na.2009.01.173 |
| [7] | Nieto, J.J., Rodriguez-Lopez, R.: Contractive mapping theorems in partially ordered sets and applications of ordinary differential equations. Order 22, 223–239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5 |
| [8] | Abkar, A., Gabeleh, M.: Best proximity point for cyclic mapping in ordered metric space. J. Optim. Theory Appl. (2011). doi: 10.1007/s10957-011-9818-2 · Zbl 1246.54034 |
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