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KKM mappings in metric type spaces. (English) Zbl 1321.54085
Summary: We discuss some recent results about KKM mappings in cone metric spaces. We also discuss the fixed point existence results of multivalued mappings defined on such metric spaces. In particular, we show that most of the new results are merely copies of the classical ones and do neither necessitate the underlying Banach space nor the associated cone.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology
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##### 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. 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, Pasquale, Common fixed points in cone metric spaces, Rend. circ. mat. Palermo. ser. II, tomo LVI, 464-468, (2007) · Zbl 1196.54086 [5] Quillot, A., An application of the Helly property to the partially ordered sets, J. combin. theory ser. A, 35, 185-198, (1983) [6] Jawhari, E.; Misane, D.; Pouzet, M., Retracts: graphs and ordered sets from the metric point of view, Contemp. math., 57, 175-226, (1986) [7] Turkoglu, D.; Abuloha, M.; Abdeljawad, T., KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear anal. TMA, 72, 348-353, (2010) · Zbl 1197.54076 [8] Khamsi, M.A.; Kirk, W.A., An introduction to metric spaces and fixed point theory, (2001), John Wiley New York · Zbl 1318.47001 [9] Robinson, D.W.; Yamamuro, S., Addition of an identity to an ordered Banach space, J. aust. math. soc. ser. A, 35, 200-210, (1983) · Zbl 0527.46016 [10] M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. (2010) doi:10.1155/2010/315398. · Zbl 1194.54065 [11] Khamsi, M.A.; Kozlowski, W.K.; Reich, S., Fixed point theory in modular function spaces, Nonlinear anal., 14, 935-953, (1990) · Zbl 0714.47040 [12] Fan, K., A generalization of tychonoffs fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701 [13] Khamsi, M.A., KKM and Ky Fan theorems in hyperconvex spaces, J. math. anal. appl., 204, 298-306, (1996) · Zbl 0869.54045 [14] 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 [15] Chang, T.H.; Yen, C.L., KKM property and fixed point theorems, J. math. anal. appl., 203, 224-235, (1996) · Zbl 0883.47067 [16] Amini, A.; Fakhar, M.; Zafarani, J., KKM mappings in metric spaces, Nonlinear anal. TMA, 60, 1045-1052, (2005) · Zbl 1076.47043 [17] 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
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