×

On Ćirić maps with a generalized contractive iterate at a point and Fisher’s quasi-contractions in cone metric spaces. (English) Zbl 1201.54032

Some classes of contraction mappings are considered. Especially the authors study so-called quasi-contraction mappings. Consequently some fixed point results are obtained by using standard methods.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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
[2] Abbas, M.; Rhoades, B. E., Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22, 511-515 (2009) · Zbl 1167.54014
[3] Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. J., 3, 133-181 (1922) · JFM 48.0201.01
[4] Bari, C. D.; Vetro, P., \( \phi \)-Pairs and common fixed points in cone metric space, Rendiconti del Circolo Matematico di Palermo, 57, 279-285 (2008) · Zbl 1164.54031
[5] Ćirić, Lj. B., A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45, 267-273 (1974) · Zbl 0291.54056
[6] Ćirić, Lj., On Seghal’s maps with a contractive iterate at a point, Publ. Instit. Math., 33, 47, 59-62 (1983) · Zbl 0529.54040
[7] Ćirić, Lj. B., Some Recent Results in Metrical Fixed Point Theory (2003), University of Belgrade: University of Belgrade Beograd
[8] Fisher, B., Quasi-contractions on metric spaces, Proc. Am. Math. Soc., 75, 321-325 (1979) · Zbl 0411.54049
[9] Guseman, L. F., Fixed point theorems for mappings with a contractive iterate at a point, Proc. Am. Math. Soc., 26, 615-618 (1970) · Zbl 0203.25202
[10] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag · Zbl 0559.47040
[11] Huang, L. G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332, 2, 1468-1476 (2007) · Zbl 1118.54022
[12] Ilić, D.; Rakočević, V., Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341, 876-882 (2008) · Zbl 1156.54023
[13] Ilić, D.; Rakočević, V., Quasi-contraction on cone metric space, Appl. Math. Lett., 22, 728-731 (2009) · Zbl 1179.54060
[15] Kadelburg, Z.; Radenović, S.; Rakočević, V., Remarks on quasi-contraction on a cone metric space, Appl. Math. Lett. (2009) · Zbl 1180.54056
[16] Krasnoselskii, M. A.; Zabreiko, P. P., Geometrical Methods in Nonlinear Analysis (1984), Springer
[17] Rezapour, Sh.; Hamlbarani Haghi, 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
[19] Sehgal, V. M., A fixed point theorem for mappings with a contractive iterate, Proc. Am. Math. Soc., 23, 631-634 (1969) · Zbl 0186.56503
[22] Zabreiko, P. P., K-metric and K-normed spaces: survey, Collect. Math., 48, 825-859 (1997) · Zbl 0892.46002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.