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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)

Citations:

Zbl 1118.54022
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References:

[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 · Zbl 0830.46001
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