Nonlinear contraction theorems in probabilistic spaces. (English) Zbl 1135.54315
The main result of the paper is a nonlinear contraction case of the common fixed point theorem of [G. Jungck, Am. Math. Mon. 83, 261–263 (1976; Zbl 0321.54025)].
Reviewer: Dorel Miheţ (Timişoara)
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E70 | Probabilistic metric spaces |
| 47H10 | Fixed-point theorems |
Citations:
Zbl 0321.54025References:
| [1] | Alsina, C.; Schweizer, B.; Sklar, A., On the definition of a probabilistic normed space, Aequationes Math., 46, 91-98 (1993) · Zbl 0792.46062 |
| [2] | Alsina, C.; Schweizer, B.; Sklar, A., Continuity properties of probabilistic norms, J. Math. Anal. Appl., 208, 446-452 (1997) · Zbl 0903.46075 |
| [3] | Bharucha-Reid, A., Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82, 641-657 (1976) · Zbl 0339.60061 |
| [4] | Chang, S. S.; Cho, Y. J.; Kang, S. M., Nonlinear Operator Theory in Probabilistic Metric Spaces (2001), Nova Science Publishers Inc.: Nova Science Publishers Inc. New York · Zbl 1080.47054 |
| [5] | Hadžić, O.; Pap, E., Fixed Point Theory in PM Spaces (2001), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht |
| [6] | Hadžić, O.; Pap, E., New classes of probabilistic contractions and applications to random operators, (Cho, Y. J.; Kim, J. K.; Kong, S. M., Fixed Point Theory and Application, vol. 4 (2003), Nova Science Publishers: Nova Science Publishers Hauppauge, New York), 97-119 · Zbl 1069.54026 |
| [7] | Jungck, G., Commuting maps and fixed points, Amer. Math. Monthly, 83, 261-263 (1976) · Zbl 0321.54025 |
| [8] | Khamsi, M. A.; Kreinovich, V. Y., Fixed point theorems for dissipative mappings in complete probabilistic metric spaces, Math. Jpn., 44, 513-520 (1996) · Zbl 0904.54033 |
| [9] | Razani, A.; Shirdaryazdi, M., Some results on fixed points in the fuzzy metric space, J. Appl. Math. Comput., 20, 401-408 (2006) · Zbl 1095.47061 |
| [10] | Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), Elsevier, North-Holland: Elsevier, North-Holland New York · Zbl 0546.60010 |
| [11] | Šerstnev, A. N., On the motion of a random normed space, Dokl. Akad. Nauk SSSR, 149, 280-283 (1963), English translation in Soviet Math. Dokl. 4 (1963) 388-390 · Zbl 0127.34902 |
| [12] | Singh, B.; Jain, S., A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301, 439-448 (2005) · Zbl 1068.54044 |
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.
