SOME FIXED POINT THEOREMS IN CONE RANDOM METRIC SPACE USING RANDOM OPERATORS
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Abstract
 Some fixed point theorems in cone random metric space by use of random operators with different contractions are proved which are generalizations of contraction mappings considered by various researchers.
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AMS CLASSIFICATION: 47H10, 54H25.
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References
. Agarwal, R.P. and O’Regan, D., Fixed point theory for generalized
Contractions on spaces with two metrics, J. Math. Anal. Appl. 248 (2000),
–414.
Beg, I. and Azam, A., J. Austral. Math. Soc. Ser. A, 53 (1992) 313-26.
Beg, I. and Shahzad, N., Nonlinear Anal., 20 (1993) 835-47.
Beg, I. and Shahzad, N., J. Appl. Math. and Stoch. Anal. 6 (1993) 95-106.
Beg, I. and Shahzad, N., Random fixed points of weakly inward operators
in conical shells, J. Appl. Math. Stoch. Anal. 8 (1995), 261–264.
Beiranvand, A., Moradi, S., Omid M.and Pazandeh H., Two Fixed Point
Theorems For Special Mappings, arXiv:0903.1504v1 math.FA, (2009).
Berinde, V., Iterative approximation of fixed points, Lecture Notes in
Mathematics, 1912,Springer, Berlin, 2007.
Bharucha-Reid, A. T., “Random Integral Equationsâ€, Academic press,
New York, 1972.
Chen, J., Li, Z., Common Fixed Points For Banach Operator Pairs in Best
Approximation, J.Math. Anal. Appl., 336(2007), 1466-1475.
Dhagat, V.B., Sharma, A.K., Bharadwaj, R.K., Fixed point theorem for
Random operators in Hilbert Spaces, International Journal of Mathema -
tical Analysis 2 no.12 (2008), 557-561.
Hans, O., Reduzierende, Czech. Math. J. 7 (1957) 154-58.
Hans, O., Random operator equations, Proc. 4th Berkeley Symp. Math.
Statist. Probability (1960), Vol. II, (1961) 180-202.
Hardy, G. E. and Rogers, T. D., Canad. Math. Bull., 16 (1973) 201-206.
Huang, L.G., Zhang, X., Cone metric spaces and a fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476.
Itoh, S., Random fixed point theorems with an application to random
differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979),
–273.
Kannan, R., Some results on fixed points. Bull.Calcutta Math.Soc., 10, 71-76 (1968).
Pathak, H.K., Shahzad, N., Fixed point results for generalized quasi-
contraction mappings in abstract metric spaces, Nonlinear Anal. 71
(2009), 6068- 6076.
Kuratowski, K. and Ryll-Nardzewski, C., A general theorem on selectors,
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 379–
Lin, T.C., Random approximations and random fixed point theorems for
continuous 1-set-contractive random maps, Proc. Amer. Math. Soc. 123
(1995), 1167–1176.
Mehta Smrati, Singh A. D., Sanodia and Dhagat Vanita Ben, “Fixed
point theorems for weak contraction in cone random metric spacesâ€,
Bull. Cal. Math. Soc.,103(4)pp 303-310,2011.
O’Regan, D., A continuation type result for random operators, Proc.
Amer. Math. Soc. 126 (1998), 1963–1971.
Papageorgiou, N.S., Random fixed point theorems for measurable Multi-
functions in Banach spaces, Proc. Amer. Math. Soc. 97 (1986), 507–514.
Rezapour, Sh., Hamlbarani, R., Some notes on the paper â€Cone metric
spaces and fixed points theorems of contractive mappingsâ€, J. Math.
Anal. Appl. 345 (2008), 719-724.
Rezapour, Sh., Haghi, R.H., Shahzad, N., Some notes on fixed points of quasi- contraction map, Applied Mathematics Letters, 23 (2010) 498-502.
Rhoades, B. E., Sessa, S., Khan, M. S. and Swaleh, M., J. Austral. Math.
Soc. ( Ser. A) 43 (1987) 328-46.
Sehgal, V. M. and Singh, S. P. Proc. Amer. Math. Soc., 95(1985) 91-94.
Shahzad, N. and Latif, S., Random fixed points for several classes of 1-
ball -contractive and 1-set-contractive random maps, J. Math. Anal.
Appl. 237 (1999), 83–92.
Spacek, A. Zufallige Gleichungen, Czechoslovak Math. J. 5 (1955) 462-
Sumitra, V.R., Uthariaraj,R. Hemavathy, Common Fixed Point Theorem For T- Hardy-Rogers Contraction Mapping in a Cone Metric Space, International Mathematical Forum5(2010), 1495-1506.