Some Random Fixed Point Theorems for (q,L)-Weak Contractions ABSTRACT | FULL TEXT

Year 2012, Volume: 41 Issue: 6, 795 - 812, 01.06.2012

Mantu Saha Debashis Dey

Keywords

-

References

• Aage, C. T. and Salunke, J. N. On common fixed points for contractive type mappings in cone metric spaces, Bull. Math. Anal. Appl. 1 (3), 10–15, 2009.
• Achari, J. On a pair of random generalized non-linear contractions, Int. J. Math. Math. Sci. 6 (3), 467–475, 1983.
• Arens, R. F. A topology for spaces of transformations, Annals of Math. 47 (2), 480–495, Banach, S. Sur les op´erations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3, 133–181, 1922.
• Berinde, V. Approximating fixed points of weak contractions using Picard iteration Nonlin- ear Anal. Forum 9 (1), 43–53, 2004.
• Berinde, V. Iterative approximation of fixed points (Springer-Verlag, Berlin, 2007).
• Berinde, V. Approximating common fixed points of noncommuting almost contractions in metric spaces, Fixed Point Theory 11 (2), 179–188, 2010.
• Berinde, V. General constructive fixed point theorems for ´Ciri´c-type almost contractions in metric spaces, Carpathian J. Math. 24 (2), 10–19, 2008.
• Bharucha-Reid, A. T. Random integral equations (Academic Press, New York, 1972).
• Bharucha-Reid, A. T. Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. (5), 641–657, 1976.
• Chatterjea, S. K. Fixed point theorems, C. R. Acad. Bulgare Sci. 25, 727–730, 1972.
• ´Ciri´c, Lj. B. A generalization of BanachÆs contraction principle, Proc. Am. Math. Soc. 45, –273, 1974.
• Hanˇs, O. Reduzierende zuf¨allige transformationen, Czechoslovak Math. Journal 7 (82), 154– , 1957.
• Hanˇs, O. Random operator equations, Proceedings of 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, University of California Press, California, part I, 185–202, 1961.
• Hicks, T. L. and Rhoades, B. E. A Banach type fixed point theorem, Math. Japonica 24 (3), –330, 1979.
• Itoh, S. Random fixed-point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (2), 261–273, 1979.
• Ivanov, A. A. Fixed points of metric space mappings (in Russian), Isledovaniia po topologii. II, Akademia Nauk, Moskva, 5–102, 1976.
• Joshi, M. C. and Bose, R. K. Some Topics in Non Linear Functional Analysis (Wiley Eastern Ltd., New Delhi, 1984).
• Kannan, R. Some results on fixed points, Bull. Cal. Math. Soc. 60, 71–76, 1968.
• Lahiri, B. K. and Das, P. Fixed point of Ljubomir ´Ciri´c’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen 61 (3-4), 589–594, 2002.
• Lee, A. C. H. and Padgett, W. J. On random nonlinear contraction, Math. Systems Theory ii, 77–84, 1977.
• Mukherjee, A. Transformation aleatoives separables theorem all point fixed aleatoire, C. R. Acad. Sci. Paris Ser. A-B 263, 393–395, 1966.
• Padgett, W. J. On a nonlinear stochastic integral equation of the Hammerstein type, Proc. Amer. Math. Soc. 38, (1), 1973.
• Rhoades, B. E. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226, 257–290, 1977.
• Rhoades, B. E. Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196, –176, 1974.
• Rhoades, B. E. Contractive definitions and continuity, Contemp. Math. 72, 233–245, 1988.
• Rothe, E. Zur Theorie der topologische ordnung und der vektorfelder in Banachschen Rau- men, Composito Math. 5, 177–197, 1937.
• Rus, I. A. Some fixed point theorems in metric spaces, Rend. Ist. Matem. Univ. di Trieste , 169–172, 1971.
• Rus, I. A. On the method of successive approximations (in Russian), Revue Roum. Math. Pures Appl. 17, 1433–1437, 1972.
• Rus, I. A. Principles and applications of the fixed point theory (in Romanian) (Editura Dacia, Cluj-Napoca, 1979).
• Saha, M. On some random fixed point of mappings over a Banach space with a probability measure, Proc. Nat. Acad. Sci., India 76 (A)III, 219–224, 2006.
• Saha, M. and Debnath, L. Random fixed point of mappings over a Hilbert space with a probability measure, Adv. Stud. Contemp. Math. 1, 79–84, 2007.
• Sehgal, V. M. and Waters, C. Some random fixed point theorems for condensing operators, Proc. Amer. Math. Soc. 90 (1), 425–429, 1984. ˇSpaˇcek, A. Zuf¨allige Gleichungen, Czechoslovak Mathematical Journal 5 (80), 462–466,
• Taskovic, M. Osnove teorije fiksne tacke (Fundamental Elements of Fixed Point Theory) (Matematicka biblioteka 50, Beograd, 1986).
• Yosida, K. Functional analysis (Academic Press, New york, Springer-Verlag, Berlin, 1965).
• Zamfirescu, T. Fixed point theorems in metric spaces, Arch. Math. (Basel) 23, 292–298,