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Common fixed point theorems for \(c\)-distance in ordered cone metric spaces. (English) Zbl 1231.54028
Summary: Recently, Y. J. Cho, R. Saadati and S. H. Wang [Comput. Math. Appl. 61, No. 4, 1254–1260 (2011; Zbl 1217.54041)] introduced the concept of the \(c\)-distance in a cone metric space and established some fixed point theorems on \(c\)-distance. The aim of this paper is to extend and generalize the main results of [loc. cit.] and also show some examples to validate our main results.

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)
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[1] Banach, S., Sur LES opérations dans LES ensembles abstraits et leurs applications aux équations intégrales, Fund. math., 3, 133-181, (1922) · JFM 48.0201.01
[2] Arvanitakis, A.D., A proof of the generalized Banach contraction conjecture, Proc. amer. math. soc., 131, 12, 3647-3656, (2003) · Zbl 1053.54047
[3] Boyd, D.W.; Wong, J.S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 458-464, (1969) · Zbl 0175.44903
[4] Choudhury, B.S.; Das, K.P., A new contraction principle in Menger spaces, Acta math. sin., 24, 8, 1379-1386, (2008) · Zbl 1155.54026
[5] Merryfield, J.; Rothschild, B.; Stein, J.D., An application of ramsey’s theorem to the Banach contraction principle, Proc. amer. math. soc., 130, 4, 927-933, (2002) · Zbl 1001.47042
[6] Sintunavart, W.; Kumam, P., Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition, Appl. math. lett., 22, 1877-1881, (2009) · Zbl 1225.54028
[7] Sintunavart, W.; Kumam, P., Weak condition for generalized multi-valued \((f, \alpha, \beta)\)-weak contraction mappings, Appl. math. lett., 24, 460-465, (2011) · Zbl 1206.54064
[8] Sintunavart, W.; Kumam, P., Coincidence and common fixed points for generalized contraction multi-valued mappings, J. comput. anal. appl., 13, 2, 362-367, (2011) · Zbl 1221.47095
[9] Sintunavart, W.; Kumam, P., Gregus-type common fixed point theorems for tangential multivalued mappings of integral type in metric spaces, Int. J. math. math. sci., 2011, (2011), Article ID 923458, 12 pages · Zbl 1215.54026
[10] Sintunavart, W.; Kumam, P., Gregus type fixed points for a tangential multi-valued mappings satisfying contractive conditions of integral type, J. inequal. appl., 2011, 3, (2011) · Zbl 1288.54044
[11] Suwannawit, J.; Petrot, N., Common fixed point theorems for hybrid generalized multivalued, Thai J. math., 9, 2, 411-421, (2011)
[12] Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. amer. math. soc., 136, 5, 1861-1869, (2008) · Zbl 1145.54026
[13] 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
[14] Abbas, M.; Jungck, G., Common fixed point results for noncommuting mappings without continuity in cone metric space, J. math. anal. appl., 341, 416-420, (2008) · Zbl 1147.54022
[15] Abbas, M.; Rhoades, B.E., Fixed and periodic point results in cone metric spaces, Appl. math. lett., 22, 511-515, (2009) · Zbl 1167.54014
[16] Azam, A.; Arshad, M., Common fixed points of generalized contractive maps in cone metric space, Bull. Iranian math. soc., 35, 2, 225-264, (2009) · Zbl 1201.47052
[17] Ilić, D.; Rakočević, V., Common fixed point for maps on cone metric space, J. math. anal. appl., 341, 876-882, (2008) · Zbl 1156.54023
[18] Ilić, D.; Rakočević, V., Quasi-contraction on a cone metric space, Appl. math. lett., 22, 728-731, (2009) · Zbl 1179.54060
[19] Wardowski, D., Endpoint and fixed points of set-valued contractions in cone metric spaces, Nonlinear anal., 71, 512-516, (2009) · Zbl 1169.54023
[20] Cho, Y.J.; Saadati, R.; Wang, S.H., Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. math. appl., 61, 1254-1260, (2011) · Zbl 1217.54041
[21] Jungck, G.; Radenović, S.; Radojević, S.; Rakočević, V., Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed point theory appl., (2009), Article ID 643840, 13 pages · Zbl 1190.54032
[22] Kada, O.; Suzuki, T.; Takahashi, W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. japon., 44, 381-391, (1996) · Zbl 0897.54029
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