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The aim of this paper is to study weak and strong convergence of an implicit random iterative process with errors to a common random fixed point of two finite families of asymptotically nonexpansive random mappings in a uniformly convex separable Banach space.
Czasopismo
Rocznik
Tom
Strony
129--148
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
- Department of Mathematics University of Assiut P.O. Box 71516, Assiut, Egypt
autor
- Department of Mathematics University of Assiut P.O. Box 71516, Assiut, Egyp
Bibliografia
- [1] Banerjee S., Choudhury B.S., Composite implicit random iterations for approximating common random fixed point for a finite family asymptotically nonexpansive random operators, Commun. Korean Math. Soc., 26(1)(2011), 23-35.
- [2] Beg I., Approximaton of random fixed points in normed spaces, Nonlinear Anal., 51(2002), 1363-1372.
- [3] Beg I., Minimal displacement of random variables under Lipschitz random maps, Topol. Methods Nonlinear Anal., 19(2002), 391-397.
- [4] Beg I., Random fixed points of random operators satisfying semicontractivity conditions, Math. Japan., 46(1997), 151-155.
- [5] Beg I., M. Abbas M., Iterative procedure for solutions of random operator equations in Banach spaces, J. Math. Appl., 315(2006), 181-201.
- [6] Beg I., Abbas M., Random fixed point theorems for a random operator on an unbounded subset of a Banach space, Appl. Math. Lett., 21(10)(2008), 1001-1004.
- [7] Beg I., Shahzad N., Random fixed point theorems for nonepansive and contractive type random operators on Banach spaces, J. Appl. Math. Stochastic Anal., 7(1994), 569-580.
- [8] Bharucha-Reid A.T., Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82(1976), 641-657.
- [9] Choudhury B.S., A random fixed point iteration for three random operators on uniformly convex Banach spaces, Analysis in Theory and Application, 19(2)(2003), 99-107.
- [10] Choudhury B.S., Convergence of a random iteration scheme to a random fixed point, J. Appl. Math. Stochastic Anal., 8(2)(1995), 139-142.
- [11] Chang S.S., Cho Y.J., Zhou H., Demi-closed principle and weak convergence problems for asymptotically nonexpansive mappings, J. Korean Math. Soc., 38(2001), 1245-1260.
- [12] Cianciaruso F., Marino G., Wang X., Weak and strong convergence of the Ishikawa iterative process for a finite family of asymptotically nonexpansive mappings, Appl. Math. Comput., 216(2010), 3558-3567.
- [13] Goebel K., Kirk W.A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174.
- [14] Hans O., Reduzierende zulliallige transformaten, Czechoslovak Math. J., 7(1957), 154-158.
- [15] Hans O., Random operator equations, Proceedings of the fourth Berkeley Symposium on Math. Statistics and Probability II, (1961), 185-202.
- [16] Hao Y., Wang X., Tong A., Weak and strong convergence theorems for two finite families of asymptotically nonexpansive mappings in Banch spaces, Advances in Fixed Point Theory, 2(4)(2012), 417-432.
- [17] Itoh S., Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67(1979), 261-273.
- [18] Opial Z., Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73(1967), 591-597.
- [19] Papageorgiou N.S., Random fixed point theorems for measurable multifunction in Banach spaces, Proc. Amer. Math. Soc., 97(1986), 507-514.
- [20] Plubtieng S., Kumam P., Wangkeeree R., Approximation of a common random fixed point for a finite family of random operators, Int. J. Math. Math. Sci., 2007(2007) 1-12. D0I:10.1155/2007/69626.
- [21] Plubtieng S., Kumam P., Wangkeeree R., Random three-step iteration scheme and common random fixed point of three operators, J. Appl. Math. Stoch. Anal., 2007(2007), 1-10.
- 22] Plubtieng S., Wangkeeree R., Punpaeng R., On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 322(2006), 1018-1029.
- [23] Saluja A.S., Rashwan R.A., Jhade P.K., Approximating common fixed points of finite family of asymptotically nonexpansive non-self mappings, Bulletin Inter. Math. Virtual Institute, 2(2012), 195-204.
- [24] Schu J., Weak and strong convergence to fixed points of asymptotically non-expansive mappings, Bull. Austral. Math. Soc., 43(1991), 153-159.
- [25] Spacek A., Zufallige gleichungen, Czechoslovak Math. J., 5(1955), 462-466.
- [26] Suantai S., Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 311(2005), 506-517.
- [27] Sun Z., Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl., 286(1)(2003), 351-358.
- [28] Tan K.K., Xu K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178(2)(1993), 301-308.
- [29] Xu H.K., Some random fixed point theorems for condensing and nonexpansive operators, Proc. Amer. Math. Soc., 110(1990), 103-123.
- [30] Xu H.K., Ori R.G., An implicit iteration process for nonexpansive mappings, Numerical Functional Analysis and Optimization, 22(2001), 767-773.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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