×

Fixed point theory in symmetric spaces with applications to probabilistic spaces. (English) Zbl 0947.54022

The main purpose of this paper is to present Jungck type fixed point theorems [G. Jungck, Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54025); the reviewer, Math. Semin. Notes, Kobe Univ. 7, 91-97 (1979; Zbl 0419.54029)] in general probabilistic structures. Indeed, the authors obtain common fixed point theorems for symmetric spaces and then present these results in probabilistic analysis. Subsequently, several results from G. Jungck [loc. cit.], the first author [Math. Jap. 44, No. 3, 487-493 (1996; Zbl 0868.47048)], the reviewer [loc. cit.] and elsewhere are generalized.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E70 Probabilistic metric spaces
47H10 Fixed-point theorems
47S50 Operator theory in probabilistic metric linear spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Choudhury, B. S., Some results in fixed point theory, Bull. Cal. Math. Soc., 86, 47-58 (1994) · Zbl 0822.54032
[2] Constantin, G.; Istrǎteseu, I., Elements of Probabilistic Analysis (1989), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0694.60002
[3] Hicks, T. L., Fixed point theorems for d-complete topological spaces I, Internat. J. Math. & Math. Sci., 15, 435-440 (1992) · Zbl 0773.54027
[4] Hicks, T. L.; Rhoades, B. E., Fixed point theorems for d-complete topological spaces II, Math. Japonica, 37, 847-853 (1992) · Zbl 0773.54026
[5] Hicks, T. L.; Rhoades, B. E., Fixed point theorems for pairs of mappings in d-complete topological spaces, Internat. J. Math. & Math. Sci., 16, 259-266 (1993) · Zbl 0796.54049
[6] Hicks, T. L., Fixed point theorem in F-complete topological spaces, Far East J. Math. Sci., 3, 2, 205-213 (1995) · Zbl 0942.47045
[7] Hicks, T. L., Random normed linear structures, Math. Japonica, 44, 3, 483-486 (1996) · Zbl 0868.46059
[8] Hicks, T. L., Fixed point theory in probabilistic metric spaces II, Math. Japonica, 44, 3, 487-493 (1996) · Zbl 0868.47048
[9] Jachymski, J.; Matkowski, J.; Swiatkowski, T., Nonlinear contractions on semimetric spaces, J. Appl. Anal., 1, 125-134 (1995) · Zbl 1295.54055
[10] Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83, 261-263 (1976) · Zbl 0321.54025
[11] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), North-Holland: North-Holland Amsterdam · Zbl 0546.60010
[12] Schweizer, B.; Sherwood, H.; Tardiff, R. M., Contraction on probabilistic metric spaces, Examples and counter examples, Stochastica, 12, 1, 5-17 (1988) · Zbl 0689.60019
[13] V. Radu, Some fixed point theorems in probabilistic metric spaces, Lecture Notes in Math., vol. 1233, Springer, Berlin, 1987, pp 125-133.; V. Radu, Some fixed point theorems in probabilistic metric spaces, Lecture Notes in Math., vol. 1233, Springer, Berlin, 1987, pp 125-133. · Zbl 0622.60008
[14] Pap, E.; Hadžić, O.; Mesiar, R., A fixed point theorem in probabilistic metric spaces and an application, J. Math. Anal. Appl., 202, 433-449 (1996) · Zbl 0855.54043
[15] Stojaković, M., A common fixed point theorem for the commuting mappings, Indian J. Pure Appl. Math., 17, 4, 466-475 (1986) · Zbl 0591.54033
[16] Stojaković, M., Common fixed point theorems in complete metric and probabilistic metric spaces, Bull. Austral. Math. Soc., 36, 73-88 (1988) · Zbl 0601.54056
[17] Wilson, W. A., On semi-metric spaces, Amer. J. Math., 53, 361-373 (1931)
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.