Random fixed point theorems for Ciric quasi contraction in cone random metric spaces

Saluja, G. S.

doi:10.1515/awutm-2015-0009

Abstract

The purpose of this paper is to establish a common random fixed point theorem by using Ciric quasi contraction for two random operators in the framework of cone random metric spaces and also to obtain some random fixed point results as corollaries. Our results extend and generalize the corresponding recent result from the current existing literature.

References

[1] M. Abbas and G. Jungck, Common fixed point results for non commuting map- pings without continuity in cone metric spaces, J. Math. Anal. Appl., 341, (2008), 416-42010.1016/j.jmaa.2007.09.070
Search in Google Scholar
[2] M. Arshad and P. Vetro A. Azam, On Edelstein type multivalued random op- erators, Hacet. J. Math. Stat., 42(3), (2013), 223-229
Search in Google Scholar
[3] M. Arshad and A. Shoaib, Fixed points of multivalued mappings in fuzzy metric spaces, Proceedings of the world congress on engineering, July 4-6, (2012), p.664-664
Search in Google Scholar
[4] I. Beg, Random fixed points of random operators satisfying semicontractivity con- ditions, Mathematics Japonica, 46(1), (1997), 151-155
Search in Google Scholar
[5] I. Beg, Approximation of random fixed points in normed spaces, Nonlinear Anal., 51(8), (2002), 1363-137210.1016/S0362-546X(01)00902-6
Search in Google Scholar
[6] I. Beg and M. Abbas, Equivalence and stability of random fixed point iterative procedures, J. Appl. Math. Stoch. Anal., (2006), (2006), 1910.1155/JAMSA/2006/23297
Search in Google Scholar
[7] I. Beg and M. Abbas, Iterative procedures for solutions of random operator equa- tions in Banach spaces, J. Math. Anal. Appl., 315(1), (2006), 181-20110.1016/j.jmaa.2005.05.073
Search in Google Scholar
[8] A.T. Bharucha-Reid, Random Integral equations Mathematics in Science and En- gineering, J. Math. Anal. Appl., 96, (1972), .
Search in Google Scholar
[9] A.T. Bharucha-Reid, Fixed point theorems in Probabilistic analysis, Bull. Amer. Math. Soc., 82(5), (1976), 641-65710.1090/S0002-9904-1976-14091-8
Search in Google Scholar
[10] L.B. Ciric, A generalization of Banach principle, Proc. Amer. Math. Soc., 45, (1974), 727-73010.2307/2040075
Search in Google Scholar
[11] S.K. Chatterjee, Fixed point theorems compactes, Rend. Acad. Bulgare Sci., 25, (1972), 727-730
Search in Google Scholar
[12] O. Hanš, Reduzierende zufallige transformationen, Czech. Math. J., 7(82), (1957), 154-15810.21136/CMJ.1957.100238
Search in Google Scholar
[13] O. Hanš, Random operator equations, Proceeding of the 4th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, California, II, (1961), 185-202
Search in Google Scholar
[14] C.J. Himmelberg, Measurable relations, Fund. Math., 87, (1975), 53-7210.4064/fm-87-1-53-72
Search in Google Scholar
[15] L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332(2), (2007), 1468-147610.1016/j.jmaa.2005.03.087
Search in Google Scholar
[16] D. Ilic and V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341, (2008), 876-88210.1016/j.jmaa.2007.10.065
Search in Google Scholar
[17] S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67(2), (1979), 261-27310.1016/0022-247X(79)90023-4
Search in Google Scholar
[18] R. Kannan, Some results on fixed point theorems, Bull. Cal. Math. Soc., 60, (1969), 71-78
Search in Google Scholar
[19] A.D. Singh and Vanita Ben Dhagat Smriti Mehta, Fixed point theorems for weak contraction in cone random metric spaces, Bull. Cal. Math. Soc., 103(4), (2011), 303-310
Search in Google Scholar
[20] N.S. Papageorgiou, Random fixed point theorems for measurable multifunctions in Banach spaces, Proc. Amer. Math. Soc., 97(3), (1986), 507-51410.1090/S0002-9939-1986-0840638-3
Search in Google Scholar
[21] N.S. Papageorgiou, On measurable multifunctions with stochastic domain, J. Aus- tra. Math. Soc. Series A, 45(2), (1988), 204-21610.1017/S1446788700030111
Search in Google Scholar
[22] R. Penaloza, A characterization of renegotiation proof contracts via random fixed points in Banach spaces, working paper 269, Department of Economics, University of Brasilia, Brasilia, December, (2002)
Search in Google Scholar
[23] A. Petrusel, Generalized multivalued contractions, Nonlinear Anal. (TMA), 47(1), (2001), 649-65910.1016/S0362-546X(01)00209-7
Search in Google Scholar
[24] G. Petrusel and A. Petrusel, Multivalued contractions of Feng-Liu type in com- plete gauge spaces, Carpth. J. Math. Anal. Appl., 24, (2008), 392-396
Search in Google Scholar
[25] Sh. Rezapour and R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings", J. Math. Anal. Appl., 345(2), (2008), 719-72410.1016/j.jmaa.2008.04.049
Search in Google Scholar
[26] V.M. Sehgal and S.P. Singh, On random approximations and a random fixed point theorem for set valued mappings, Proc. Amer. Math. Soc., 95(1), (1985), 91-9410.1090/S0002-9939-1985-0796453-1
Search in Google Scholar
[27] P. Vetro, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo (2), 56(3), (2007), 464-46810.1007/BF03032097
Search in Google Scholar
[28] D.H. Wagner, Survey of measurable selection theorem, SIAM J. Control Optim., 15(5), (1977), 859-90310.1137/0315056
Search in Google Scholar
[29] P.P. Zabrejko, K-metric and K-normed linear spaces: survey, Collec. Math., 48(4-6), (1997), 825-859
Search in Google Scholar
[30] T. Zamffirescu, Fixed point theorems in metric space, Arch. Math. (Basel), 23, (1972), 292-29810.1007/BF01304884
Search in Google Scholar

Random fixed point theorems for Ciric quasi contraction in cone random metric spaces

Abstract

Paradigm

My account