×

zbMATH — the first resource for mathematics

KKM mappings in cone \(b\)-metric spaces. (English) Zbl 1231.54022
Summary: We establish some topological properties of the cone \(b\)-metric spaces and then improve some recent results about KKM mappings in the setting of a cone \(b\)-metric space. We also prove some fixed point existence results for multivalued mappings defined on such spaces.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Long-Guang, H.; Xian, Z., Cone metric spaces and fixed point theorems of contractive mappings, J. math. anal. appl., 332, 1468-1476, (2007) · Zbl 1118.54022
[2] Rzepecki, B., On fixed point theorems of maia type, Publ. de l’inst. math., 28, 42, 179-186, (1980) · Zbl 0482.47029
[3] Turkoglu, D.; Abuloha, M., Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta math. sin. (engl. ser.), 26, 3, 489-496, (2010) · Zbl 1203.54049
[4] Vetro, P., Common fixed points in cone metric spaces, Rend. circ. mat. Palermo. serie II, tomo LVI, 464-468, (2007) · Zbl 1196.54086
[5] Khamsi, M.A.; Hussain, N., KKM mappings in metric type spaces, Nonlinear anal., 73, 3123-3129, (2010) · Zbl 1321.54085
[6] Sh. Rezapour, M. Derafshpour, R. Hamlbarani, A review on topological properties of cone metric spaces, in: Proceedings of the International Conference on Analysis, Topology and Applications, ATA ’08, Vrinjacka Banja, Serbia, May-June 2008. · Zbl 1145.54045
[7] Rezapour, Sh.; Hamlbarani, R., Some notes on the paper “cone metric spaces and fixed point theorems of contractive mappings”, J. math. anal. appl., 345, 719-724, (2008) · Zbl 1145.54045
[8] Czerwik, S., Nonlinear set-valued contraction mappings in \(b\)-metric spaces, Atti sem. mat. fiz. univ. modena, 46, 263-276, (1998) · Zbl 0920.47050
[9] Singh, S.L.; Czerwik, S.; Król, K.; Singh, A., Coincidences and fixed points of hybrid contractions, Tamsui oxf. J. math. sci., 24, 4, 401-416, (2008) · Zbl 1175.54063
[10] Khamsi, M.A., Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed point theory appl., 7, (2010), Art. ID 315398 · Zbl 1194.54065
[11] Fan, K., A generalization of tychonoff’s fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701
[12] Khamsi, M.A., KKM and Ky Fan theorems in hyperconvex spaces, J. math. anal. appl., 204, 298-306, (1996) · Zbl 0869.54045
[13] Beg, I.; Hussain, N.; Khan, A.R., Fixed point, almost fixed point and best approximation of nonexpansive multivalued mapping in Banach spaces, Adv. math. sci. appl., 13, 83-111, (2003) · Zbl 1054.47042
[14] Chang, T.H.; Yen, C.L., KKM property and fixed point theorems, J. math. anal. appl., 203, 224-235, (1996) · Zbl 0883.47067
[15] Wu, X.; Thompson, B.; Yuan, G.X., Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces, J. math. anal. appl., 276, 80-89, (2002) · Zbl 1011.54034
[16] Amini, A.; Fakhar, M.; Zafarani, J., KKM mappings in metric spaces, Nonlinear anal. TMA, 60, 1045-1052, (2005) · Zbl 1076.47043
[17] Hussain, N.; Khan, A.R.; Agarwal, Ravi P., Krasnosel’skii and Ky Fan type fixed point theorems in ordered Banach spaces, J. nonlinear convex anal., 11, 3, 475-489, (2010) · Zbl 1219.47079
[18] Turkoglu, D.; Abuloha, M.; Abdeljawad, T., KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear anal., 72, 348-353, (2010) · Zbl 1197.54076
[19] Jawhari, E.; Misane, D.; Pouzet, M., Retracts: graphs and ordered sets from the metric point of view, Contemp. math., 57, 175-226, (1986)
[20] Khamsi, M.A.; Kirk, W.A., An introduction to metric spaces and fixed point theory, (2001), John Wiley New York · Zbl 1318.47001
[21] Khamsi, M.A.; Kozlowski, W.K.; Reich, S., Fixed point theory in modular function spaces, Nonlinear anal., 14, 935-953, (1990) · Zbl 0714.47040
[22] M.H. Shah, S. Simic, N. Hussain, A. Sretenovic, S. Radenovic, Common fixed points theorems for occasionally weakly compatible pairs on cone metric type spaces, JoCAAA 28 (2011) (in press). · Zbl 1256.54081
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.