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Some generalizations of fixed point theorems in cone metric spaces. (English) Zbl 1203.54043

Author’s abstract: We generalize, extend, and improve some recent fixed point results in cone metric spaces, including the results of L. D. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)], P. Vetro [Rend. Circ. Mat. Palermo (2) 56, No. 3, 464–468 (2007; Zbl 1196.54086)], M. Abbas and G. Jungck [J. Math. Anal. Appl. 341, No. 1, 416–420 (2008; Zbl 1147.54022)], Sh.Rezapour and R.Hamlbarani [J. Math. Anal. Appl. 345, No. 2, 719–724 (2008; Zbl 1145.54045)]. In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed with. Consequently, the results generalize several fixed results in metric spaces, including the results of G. E. Hardy and T. D. Rogers [Can. Math. Bull. 16, 201–206 (1973; Zbl 0266.54015)], R. Kannan [Am. Math. Mon. 76, 405–408 (1969; Zbl 0179.28203)], G. Jungck, S. Radenović, S. Radojević and V. Rakočević [Fixed Point Theory Appl. 2009, Article ID 643840 (2009; Zbl 1190.54032), and all the references therein].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

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