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Periodic and fixed point theorems in a quasi-metric space

Part of: Nonlinear operators and their properties Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Ljubomir Ćirić
Ljubomir Ćirić
Affiliation:
Matematički InstitutKneza Mihaila 35 11000 Beograd, Yugoslavia
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Abstract

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General periodic and fixed point theorems are proved for a class of self maps of a quasi-metric space which satisfy the contractive definition (A) below. Two examples are presented to show that the class of mappings which satisfy (A) is indeed wider than a class of selfmaps which satisfy Caristi's contractive definition (C) below. Also a common fixed point theorem for a pair of maps which satisfy a contractive condition (D) below is established.

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 80 - 85
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bhakta, P. S. and Basu, T., ‘Some fixed point theorems on metric spaces’, J. Indian Math. Soc. 45 (1981), 399–404.Google Scholar
[2]Bollenbacher, A. and Hicks, T. L., ‘A fixed-point theorem revisited’, Proc. Amer. Mat. Soc. 102 (1988), 898–900.CrossRefGoogle Scholar
[3]Brondsted, A., ‘On a lemma of Bishop and Phelps’, Pacific J. Math. 55 (1974), 335–341.CrossRefGoogle Scholar
[4]Caristi, J., ‘Fixed point theorems for mappings satisfying inwardness conditions’, Trans. Amer. Math. Soc. 215 (1976), 241–251.CrossRefGoogle Scholar
[5]Ćirić, Lj., ‘On contraction type mappings’, Math. Balkanica 1 (1971), 52–57.Google Scholar
[6]Ćirić, Lj., ‘On mappings with a contractive iterate’, Publ. Inst. Math. (Beograd), 26 (40) (1979), 79–82.Google Scholar
[7]Harder, A. and Hicks, T. L., ‘Fixed point theory and iteration procedures’, Indian J. Math. 19 (1988), 17–26.Google Scholar
[8]Hicks, T. L., ‘Fixed point theorems for quasi-metric spaces’, Math. Japon. 33 (1988), 231–236.Google Scholar
[9]Hicks, T. and Rhoades, B., ‘A Banach type fixed point theorem’, Math. Japon. 24 (1979), 327–330.Google Scholar
[10]Siegel, J., ‘A new proof of Caristi's fixed point theorem’, Proc. Amer. Math. Soc. 66 (1977), 54–56.Google Scholar
[11]Stoltenberg, R. A., ‘On quasi-metric spaces’, Duke Math. J. 36 (1969), 65–71.CrossRefGoogle Scholar
[12]Wong, C. S., ‘Fixed point theorems for non-expansive mappings’, J. Math. Anal. Appl. 37 (1972), 142–150.CrossRefGoogle Scholar
[13]Wong, C. S., ‘On a fixed point theorem of contractive type’, Proc. Amer. Math. Soc. 57 (1976), 283–284.CrossRefGoogle Scholar