Generalized contraction mapping principles in probabilistic metric spaces

Acta Mathematica Hungarica

Volumn 101, Issue 1-2, 2003, Pages 131-148

  Hadzic O ^a   Pap, E ^a   Radu, V ^b  

^a UNIVERSITY OF NOVI SAD   (Serbia)

^b WEST UNIVERSITY OF TIMISOARA   (Romania)

Author keywords

Admissible subset; Fixed point; Generalized probabilistic contraction mapping; Probabilistic metric space; Random normed space; Triangular norm

Indexed keywords

EID: 0141864425     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:AMHU.0000003897.39440.d8     Document Type: Article

References (28)

1. S. S. Chang, Y. J. Cho and S. M. Kang, Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan Univ. Press (Cliengdu, 1994).
2. S. S. Chang, B. S. Lee, Y. J. Cho, Y. Q. Chen, S. M. Kang and J. S. Jung, Generalized contraction mapping principle and differential equations in probabilistic metric spaces, Proc. Amer. Math. Soc., 124 (1996). 2367-2376.
3. O. Hadžié, On the (ε, λ)-topology of probabilistic locally convex spaces, Glas. Mat., 13 (33) (1978), 293-297.
4. O. Hadzic, Some theorems on the fixed points in probabilistic metric and random normed spaces, Boll. Unione Mat. Ital., 1-B (6) (1982) 381-391.
5. O. Hadžié, Fixed Point Theory in Topological Vector Spaces (Novi Sad, 1984).
6. O. Hadžié. E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers (Dordrecht, 2001).
7. S. Hahn and F. Pötter, Über Fixpunkte kompakter Abbildungen in topologischen Vektorräumen, Studia Math., 50L (1974), 1-16.
8. T. L. Hicks, Fixed point theory in probabilistic metric spaces, Univ. u Novom Sadu, Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 13 (1983), 63-72.
9. J. Ishii, On the admissibility of function spaces, J. Fac. Sci. Hokkaido Univ. Series I, 19 (1965), 49-55.
10. V. Klee, Leray-Schauder theory without local convexity, Math. Ann., 141 (1960), 286-296.
11. E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers, Trends in Logic 8 (Dordrecht, 2000).
12. I. Kolumbán and A. Soós. Fractal functions using contraction method in probabilistic metric spaces, in: Proc. of the Int. Multidisciplinary Conf. Fractal 2002 (ed. M. M. Novak), World Sci. (2002), pp. 255-265.
13. M. A. Krasnoselski and P. P. Zabreiko, Geometricheskie metody nelineinogo analiza, Nauka (1975).
14. C. Krauthausen, Der Fixpunktsatz von Schauder in nicht notwendig konvexen Räumen sowie Anwendungen auf Hammersteinsche Gleichungen, Doktors Dissertation (Aachen, 1976).
15. Φ, Ber. Ges. f. Math. u. Datenverarb. Bonn, Nr. 61, 1972.
16. K. Menger, Statistical metric, Proc. Nat. Acad. USA, 28 (1942), 535-537.
17. M. Nagumo, Degree of mappings in convex linear topological spaces, Amer. J. Math., 73 (1951). 497-511.
18. E. Pap, O. Hadžié and R. Mesiar. A fixed point theorem in probabilistic metric spaces and applications in fuzzy set theory. J. Math. Anal. Appl., 202 (1996), 433-449.
19. E. Parau and V. Radu, Some remarks on Tardiff's fixed point theorem on Menger spaces, Portugaiiae Mathematica, 54 (1997), 431-440.
20. V. Radu, A remark on contractions on Menger spaces, Seminar on Probability Theory and Applications. Univ. of Tirmişoara, Nr. 64, 1983.
21. V. Radu. Some fixed point theorems in PM-spaces, in: Lectures Notes in Math. Nr. 1233, Springer, 1987, pp. 123-133.
22. V. Radu, Lectures on Probabilistic Analysis, West University of Timisoara (1996).
23. p(0,1) (0 < p < 1) sind zulässig, Wiss. Z. TU, Dresden, 12 (1963), 1149-1152.
24. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
25. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland (1983).
26. B. Schweizer, H. Sherwood and R. M. Tardiff, Contractions on probabilistic metric spaces. Examples and counter examples, Stochastica, 12 (1988), 5-17.
27. V. M. Sehgal and A. T. Bharucha-Reid, Fixed point of contraction mapping on PM spaces, Math. Systems Theory, 6 (1972), 97-100.
28. R. Tardiff, Contraction maps on probabilistic metric spaces, J. Math. Anal. Appl., 165 (1992), 517-523.