Coincidence point of four completely random operators satisfying generalized weak contractive conditions
DOI:
https://doi.org/10.5644/SJM.10.1.15Keywords:
Random operator, completely random operator, random fixed point, random coincidence pointAbstract
Contractive conditions were investigated by various authors (see, e.g [4], [9], [13], [24]). In [22], we introduced the notion of completely random operators and proved some properties of such operators. The purpose of this paper is to present some results on the existence of random coincidence points of four completely random operators satisfying generalized weak contractive conditions. Some applications to random fixed point theorems and random equations are given.
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T. N. Anh, Random fixed points of probabilistic contractions and applications to random equations, Vietnam. J. Math., 38 (2010), 227--235.
I. Beg and N. Shahzad, Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces, J. Appl. Math. Stoc. Anal.,7 (4) (1994), 569--580.
I. Beg and M. Abbas, Coincidence point and invariant approximation for mapping satisfying generallzed weak contractive condition, Fixed Point Theory Appl., {Vol. 2006}, {Article ID 74503} , 7 pages, 2006.
T. D. Benavides, G. L. Acedo and H. K. Xu, Random fixed points of set-valued operators, Proc. Amer. Math. Soc.,124 (3) (1996), 831--838.
A. T. Bharucha-Reid, Random Integral Equations, Academic Press, New York, 1972.
A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82 (5) (1976), 641--657.
B. S. Chouhury and N. Metiya, The point of coincidence and common fixed point for a pair mappings in cone metric spaces, Comput. Math. Appl., 60 (2010), 1686-1695.
D. Doric, Common fixed point for generalized $(psi,varphi)$-weak contractions, Appl. Math. Lett., 22 (2009), 1896-1900.
R. Fierro, C. Martnez and C. H. Morales, Random coincidence theorems and applications, J. Math. Anal. Appl., 378 (1) (2011), 213--219.
C. J. Himmelberg, Measurable relations, Fund. Math., 87 (1975), 53--72.
N. Hussain, A. Latif and N. Shafqat, Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces, J. Inequal. Appl., (2012), 2012:257.
B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683--2693.
N. Shahzad, Random approximations and random coincidence points of multivalued random maps with stochastic domain, New Zealand J. Math., 29 (1) (2000), 91--96.
N. Shahzad, Some general random coincidence point theorems, New Zealand J. Math., 33 (1) (2004), 95--103.
N. Shahzad, Random fixed points of discontinuous random maps, Math. Comput. Modelling, 41 (2005), 1431--1436.
N. Shahzad, On random coincidence point theorems, Topol. Methods Nonlinear Anal., 25 (2) (2005), 391--400.
N. Shahzad and N. Hussain, Deterministic and random coincidence point results for f-nonexpansive maps, J. Math. Anal. Appl., 323 (2006), 1038--1046.
K. K. Tan and X. Z. Yuan, On deterministic and random fixed points, Proc. Amer. Math. Soc., 119 (3) (1993), 849--856.
D. H. Thang and T. M. Cuong, Some procedures for extending random operators, Random Oper. Stoch. Equ., 17 (4) (2009), 359--380.
D. H. Thang and T. N. Anh, On random equations and applications to random fixed point theorems, Random Oper. Stoch. Equ., 18 (3) (2010), 199--212.
D. H. Thang and P. T. Anh, Random fixed points of completely random operators, Random Oper. Stoch. Equ., 21 (1) (2013), 1--20.
Chris P. Tsokos and W. J. Padgett, Random integral equations with applications to stochastic sytems. Lecture Notes in Mathematics, Vol. 233, Springer-Verlag, Berlin-New York, 1971.
Q. Zhang and Y. Song, Fixed point theory for generallzed $varphi$-weak contractions, Appl. Math. Lett., 22 (2009), 75--78.
