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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:
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Ćirić, Lj.B., A generalization of banach’s contraction principle, Proc. amer. math. soc., 45, 267-273, (1974) · Zbl 0291.54056
[2] Gajić, Lj.; Rakočević, V., Pair of non-self-mappings and common fixed points, Appl. math. comput., 187, 999-1006, (2007) · Zbl 1118.54304
[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
[4] Rakočević, V., Functional analysis, (1994), Naučna knjiga, Beograd
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