Turkoglu, Duran; Abuloha, Muhib; Abdeljawad, Thabet KKM mappings in cone metric spaces and some fixed point theorems. (English) Zbl 1197.54076 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 1, 348-353 (2010). Summary: We define KKM mappings in cone metric spaces and define \(N\mathfrak R\)-cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in [A.Amini, M.Fakhar and J.Zafarani, Nonlinear Anal., Theory Methods Appl.60, No.6 (A), 1045–1052 (2005; Zbl 1076.47043)]. Cited in 29 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:KKM property; fixed point; cone metric space; admissible set; totally bounded; minihedral cone; strongly minihedral cone; closed ball; semicontinuous; approximate fixed point property; compactly open; hyperconvex cone metric space; selection continuous Citations:Zbl 1076.47043 PDFBibTeX XMLCite \textit{D. Turkoglu} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 1, 348--353 (2010; Zbl 1197.54076) Full Text: DOI References: [1] Huang, L. G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332, 1468-1476 (2007) · Zbl 1118.54022 [2] Ilić, D.; Rakoćević, V., Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341, 876-882 (2008) · Zbl 1156.54023 [3] Abbas, M.; Jungck, G., Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341, 416-420 (2008) · Zbl 1147.54022 [4] Vetro, Pasquale, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo. Serie II, Tomo LVI, 464-468 (2007) · Zbl 1196.54086 [5] D. Turkoglu, M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin. (Engl. Ser.) (in press); D. Turkoglu, M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin. (Engl. Ser.) (in press) · Zbl 1203.54049 [6] Knaster, B.; Kuratowski, C.; Mazurkiewicz, S., Ein Beweis des fipunktsatzes fur \(n\)-dimensionale Simplexe, Fund. Math., 14, 132-137 (1929) · JFM 55.0972.01 [7] Amini, A.; Fakhar, M.; Zafarani, J., KKM mapping in metric spaces, Nonlinear Anal., 60, 1045-1052 (2005) · Zbl 1076.47043 [8] 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 [9] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag · Zbl 0559.47040 [10] Yu, Zenn-Tsuen; Lin, Lai-Jiu, Continuous selection and fixed point theorems, Nonlinear Anal., 52, 445-455 (2003) · Zbl 1033.54011 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.