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Fixed point theorem for two non-self mappings in cone metric spaces. (English) Zbl 1186.65073
Summary: We extend a fixed point theorem of Imdad and Kumar, for a pair of non-self maps, to non-normal cone spaces.

65J15Equations with nonlinear operators (numerical methods)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Huang, L. G.; Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. math. Anal. appl. 332, No. 2, 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] Ilić, D.; Rakočević, V.: Common fixed points for maps on cone metric space, J. math. Anal. appl. 341, 876-882 (2008) · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[4] Ilić, D.; Rakočević, V.: Quasi-contraction on cone metric space, Appl. math. Lett. (2008)
[5] 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 · doi:10.1016/j.jmaa.2008.04.049
[6] Deimling, K.: Nonlinear functional analysis, (1985) · Zbl 0559.47040
[7] Sh. Rezapour, A review on topological properties of cone metric spaces, Analysis, Topology and Applications 2008, Vrnjačka Banja, Serbia, from May 30 to June 4, 2008 · Zbl 1145.54045
[8] Assad, N. A.: On a fixed point theorem of kannan in Banach spaces, Tamkang J. Math. 7, 91-94 (1976) · Zbl 0356.47027
[9] Assad, N. A.; Kirk, W. A.: Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43, No. 3, 553-562 (1972) · Zbl 0239.54032
[10] Rhoades, B. E.: A fixed point theorem for some non-self-mappings, Math. japonica 23, No. 4, 457-459 (1978) · Zbl 0396.47038
[11] Imdad, M.; Kumar, S.: Rhoades -type fixed -point theorems for a pair of nonself mappings, Comput. math. Appl. 46, 919-927 (2003) · Zbl 1065.47059 · doi:10.1016/S0898-1221(03)90153-2
[12] Lj.B. Ćirić, S. Radenović, M. Rajović, J.S. Ume, Common fixed point theorems for non-self mappings in metric spaces of hyperbolic type (submitted for publication) · Zbl 1184.54040 · doi:10.1016/j.cam.2009.11.042