Coupled fixed points of mixed monotone operators on probabilistic Banach spaces
Beg, Ismat ; Latif, Abdul ; Ali, Rashid ; Azam, Akbar
Archivum Mathematicum, Tome 037 (2001), p. 1-8 / Harvested from Czech Digital Mathematics Library
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The existence of minimal and maximal fixed points for monotone operators defined on probabilistic Banach spaces is proved. We obtained sufficient conditions for the existence of coupled fixed point for mixed monotone condensing multivalued operators.

Publié le : 2001-01-01
Classification:  47H05,  47H10,  47S50 
@article{107780,
     author = {Ismat Beg and Abdul Latif and Rashid Ali and Akbar Azam},
     title = {Coupled fixed points of mixed monotone operators on probabilistic Banach spaces},
     journal = {Archivum Mathematicum},
     volume = {037},
     year = {2001},
     pages = {1-8},
     zbl = {1068.47093},
     mrnumber = {1822758},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107780}
}

Beg, Ismat; Latif, Abdul; Ali, Rashid; Azam, Akbar. Coupled fixed points of mixed monotone operators on probabilistic Banach spaces. Archivum Mathematicum, Tome 037 (2001) pp. 1-8. http://gdmltest.u-ga.fr/item/107780/

Beg I.; Rehman S.; Shahzad N. Fixed points of generalized contraction mappings on probabilistic metric spaces, Pakistan J. Statist. 8(2) (1992), 35–52. (1992) | MR 1225059 | Zbl 0770.54040

Bharucha-Reid A. T. Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), 641–657. (1976) | MR 0413273 | Zbl 0339.60061

Cain G. L., Jr.; Kasriel R. H. Fixed and periodic points of local contraction mappings on probabilistic metric spaces, Math. Systems Theory 9 (1970), 289–297. (1970) | MR 0458397

Chang S. S. Basic theory and applications of probabilistic metric spaces (I), App. Math. Mech. 9(2) (1988), 123–133. (1988) | MR 0943878

Chang S. S.; Cho Y. J.; Kang S. M. Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan University Press, Chendgu, China, 1994. (1994)

Chang S. S.; Ma Y. H. Coupled fixed points for mixed monotone condensing operators and existence theorem of the solutions for a class of functional equation arising in dynamic programming, J. Math. Anal. Appl. 160 (1991), 468–479. (1991) | MR 1126131

Egbert R. J. Products and quotients of probabilistic metric spaces, Pacific J. Math. 24 (1968), 437–455. (1968) | MR 0226690 | Zbl 0175.46601

Hadzic O. Some theorems on the fixed points in probabilistic metric and random normed spaces, Boll. Un. Mat. Ital. B(6), 1-B (1982), 381–391. (1982) | MR 0654942 | Zbl 0488.47028

Hutson V.; Pym J. S. Applications of Functional Analysis and Operator Theory, Academic Press, London, 1980. (1980) | MR 0569354 | Zbl 0426.46009

Istratescu V. I. Fixed Point Theory, D. Reidel Publishing Company, Dordrecht, 1988. (1988) | MR 0620639

Menger K. Statistical metric, Proc. Natl. Acad. Sci. USA, 28 (1942), 535–537. (1942) | MR 0007576

Schweizer B.; Sklar A. Statistical metric spaces, Pacific J. Math. 10 (1960), 313–334. (1960) | MR 0115153 | Zbl 0096.33203

Schweizer B.; Sklar A. Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics 5 1983. (1983) | MR 0790314 | Zbl 0546.60010

Sherwood H. Complete probabilistic metric spaces, Z. Wahrsch. Verw. Gebiete 20 (1971), 117–128. (1971) | MR 0317290 | Zbl 0212.19304

Stojakovic M. Fixed point theorems in probabilistic metric spaces, Kobe J. Math. 2(1) (1985), 1–9. (1985) | MR 0811797 | Zbl 0589.54059

Stojakovic M. Common fixed point theorems in complete metric and probabilistic metric spaces, Bull. Austral. Math. Soc. 36 (1987), 73–88. (1987) | MR 0897423 | Zbl 0601.54056

Sun Y. A fixed point theorem for monotone operators with applications, J. Math. Anal. Appl. 156 (1991), 240–252. (1991) | MR 1102609

Serstnev A. N. On the notion of random normed spaces, Dokl. Akad. Nauk 149 (1963), 280–283. (1963) | MR 0154320

Tan N. X. Generalized probabilistic metric spaces and fixed point theorems, Math. Nachr. 129 (1986), 205–218. (1986) | MR 0864635 | Zbl 0603.54049