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Quasi-contraction on a cone metric space. (English) Zbl 1179.54060
The authors define and study quasi-contractive mappings on a cone metric space. These mappings are a generalization of Ćirić’s quasi-contractions. A lemma and a fixed point theorem are established for such mappings. This result generalizes the results of L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)].

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
References:
[1]Ćirić, Lj.B.: A generalization of Banach’s contraction principle, Proc. amer. Math. soc. 45, 267-273 (1974) · Zbl 0291.54056 · doi:10.2307/2040075
[2]Gajić, Lj.; Rakočević, V.: Pair of non-self-mappings and common fixed points, Appl. math. Comput. 187, 999-1006 (2007) · Zbl 1118.54304 · doi:10.1016/j.amc.2006.09.143
[3]Guang, H. L.; Xian, Z.: 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
[4]Rakočević, V.: Functional analysis, (1994)