Alghamdi, Mohammad A.; Alnafei, Shahrazad H.; Radenović, Stojan; Shahzad, Naseer Fixed point theorems for convex contraction mappings on cone metric spaces. (English) Zbl 1235.54021 Math. Comput. Modelling 54, No. 9-10, 2020-2026 (2011). Summary: L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] rediscovered normal cone metric spaces and obtained the Banach contraction principle for this setting. Later on, Sh. Rezapour and R. Hamlbarani [J. Math. Anal. Appl. 345, No. 2, 719–724 (2008; Zbl 1145.54045)] showed that there are non-normal cones and that the assumption of normality is redundant. Cited in 13 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx) Keywords:cone metric space; convex contraction; fixed point PDF BibTeX XML Cite \textit{M. A. Alghamdi} et al., Math. Comput. Modelling 54, No. 9--10, 2020--2026 (2011; Zbl 1235.54021) Full Text: DOI References: [1] Banach, S., Sur le opération dans LES ensembles abstraits et leur application aux équation intégrales, Fund. math. J., 3, 133-181, (1922) · JFM 48.0201.01 [2] 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 [3] 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 [4] Istrăţescu, V.I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters — I, Ann. math. pure appl., 130, 89-104, (1982) · Zbl 0477.54033 [5] Wong, Y.-C.; Ng, K.-F., () [6] Kadelburg, Z.; Radenović, S.; Rakočević, V., Remarks on “quasi-contraction on a cone metric space”, Appl. math. lett., 22, 1674-1679, (2009) · Zbl 1180.54056 [7] Rezapour, Sh.; Haghi, R.H.; Shahzad, N., Some notes on fixed points of quasi-contraction maps, Appl. math. lett., 23, 498-502, (2010) · Zbl 1206.54061 [8] Haghi, R.H.; Rezapour, Sh., Fixed points of multifunctions on regular cone metric spaces, Expo. math., 28, 71-77, (2010) · Zbl 1193.47058 [9] Radenović, S., Common fixed points under contractive conditions in cone metric spaces, Comput. math. appl., 58, 1273-1278, (2009) · Zbl 1189.65119 [10] Z. Kadelburg, S. Radenović, B. Rosic, Strict contractive conditions and common fixed point theorems in cone metric spaces, Fixed Point Theory Appl. 2009, Article ID 173838, 14 Pages, doi:10.1155/2009/173838. [11] Di Bari, C.; Vetro, P., \(\varphi\)-pairs and common fixed points in cone metric spaces, Rend. circ. mat. Palermo, 57, 279-285, (2008) · Zbl 1164.54031 [12] Di Bari, C.; Vetro, P., Weakly \(\varphi\)-pairs and common fixed points in cone metric spaces, Rend. circ. mat. Palermo, 58, 125-132, (2009) · Zbl 1197.54060 [13] Rezapour, Sh.; Khandani, H.; Vaezpour, S.M., Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions, Rend. circ. mat. Palermo, 59, 185-197, (2010) · Zbl 1198.54087 [14] Rezapour, Sh.; Haghi, R.H., Fixed point of multifunctions on cone metric spaces, Numer. funct. anal. optim., 30, 7-8, 825-832, (2009) · Zbl 1171.54033 [15] Pathak, H.K.; Shahzad, N., Fixed point results for generalized quasicontraction mappings in abstract metric spaces, Nonlinear anal., 71, 6068-6076, (2009) · Zbl 1189.54036 [16] Jeong, G.S.; Rhoades, B.E., Maps for which \(F(T) = F(T^n)\), Fixed point theory appl., 6, 72-105, (2006) · Zbl 1147.47041 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.