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Common fixed point theorems on generalized distance in ordered cone metric spaces. (English) Zbl 1217.54041
Summary: We introduce a concept of the $c$-distance in a cone metric space and, by using the concept of the $c$-distance, prove some fixed point theorems in ordered cone metric spaces.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
65J15Equations with nonlinear operators (numerical methods)
Full Text: DOI
[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 · doi:10.1016/j.jmaa.2005.03.087
[2] 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 · doi:10.1016/j.jmaa.2007.09.070
[3] Abbas, M.; Rhoades, B. E.; Nazir, T.: Common fixed points for four maps in cone metric spaces, Appl. math. Comput. 216, 80-86 (2010) · Zbl 1197.54050 · doi:10.1016/j.amc.2010.01.003
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[6] Radenović, S.: Common fixed points under contractive conditions in cone metric spaces, Comput. math. Appl. 58, 1273-1278 (2009) · Zbl 1189.65119 · doi:10.1016/j.camwa.2009.07.035
[7] Radenović, S.; Rhoades, B. E.: Fixed point theorem for two non-self mappings in cone metric spaces, Comput. math. Appl. 57, 1701-1707 (2009) · Zbl 1186.65073 · doi:10.1016/j.camwa.2009.03.058
[8] Rezapour, S.; Hamlbarani, R.: Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. math. Anal. appl. 345, 719-724 (2008) · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
[9] Altun, I.; Durmaz, G.: Some fixed point theorems on ordered cone metric spaces, Rend. circ. Mat. Palermo 58, 319-325 (2009) · Zbl 1184.54038 · doi:10.1007/s12215-009-0026-y
[10] Altun, I.; Damnjanović, B.; Djorić, D.: Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. math. Lett. 23, 310-316 (2010) · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016
[11] Kadelburg, Z.; Pavlović, M.; Radenović, S.: Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. math. Appl. 59, 3148-3159 (2010) · Zbl 1193.54035 · doi:10.1016/j.camwa.2010.02.039
[12] Shatanawi, W.: Partially ordered cone metric spaces and coupled fixed point results, Comput. math. Appl. (2010) · Zbl 1205.54044
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