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Common fixed points under contractive conditions in cone metric spaces. (English) Zbl 1189.65119
Summary: The aim of this paper is to present coincidence point result for two mappings in cone metric space which satisfy new contractive conditions. Our results generalize fixed point theorems of G. Jungck [Am. Math. Mon. 83, 261–263 (1976; Zbl 0321.54025)], M. Abbas and G. Jungck [J. Math. Anal. Appl. 341, No. 1, 416–420 (2008; Zbl 1147.54022)] and B. Fisher [J. Univ. Kuwait, Sci. 8, 131–138 (1981; Zbl 0472.54030)] in cone metric spaces to symmetric spaces.

MSC:
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
[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. Appl. 341, 876-882 (2008) · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[4]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
[5]Deimling, K.: Nonlinear functional analysis, (1985) · Zbl 0559.47040
[6]Zhu, Jiang; Cho, Yeol Je; Kang, Shin Min: Equivalent contractive conditions in symmetric spaces, Comput. math. Appl. 50, 1621-1628 (2005) · Zbl 1080.47046 · doi:10.1016/j.camwa.2005.07.007
[7]Hicks, T. L.; Rhoades, B. E.: Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear anal. 36, 331-344 (1999) · Zbl 0947.54022 · doi:10.1016/S0362-546X(98)00002-9
[8]Jungck, G.: Commuting maps and fixed points, Amer. math. Monthly 83, 261-263 (1976) · Zbl 0321.54025 · doi:10.2307/2318216
[9]Fisher, B.: Four mappings with a common fixed point. (Arabic summary), J. univ. Kuwait sci. 8, 131-139 (1981) · Zbl 0472.54030