Abstract
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The results is also an extension of a known theorem in the corresponding non-random case.
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Chang, S.S. and Tan, K.K., Iteration Processes for Approximating Fixed Points of Operators of Monotone Type, Bull. Austral. Math. Soc., 57(1998), 433–445.
Chidume, C.E. and Osilike, M.O., Ishikawa Iteration Process for Nonlinear Lipschitz Strongly Accretive Mappings, J. Math. Anal. Appl., 192(1995), 727–741.
Chidume, C.E. and Moore, C., Fixed Point Iteration for Pseudocontractive Maps, Proc. Amer. Math. Soc., 127(1999), 1163–1170.
Choudhury, B.S., Convergence of a Random Iteration Scheme to a Random Fixed Point, J. Appl. Math. Stoc. Anal., 8(1995), 139–142.
Choudhury, B.S. and Ray, M., Convergence of an Iteration Leading to a Solution of Random Operator Equation, J. Appl. Math. Stoc. Anal., 12(1999), 161–168.
Choudhury, B.S. and Upadhyay, A., An Iteration Leading of Random Solutions and Fixed Points of Operators, Soochow J. Math., 25(1999), 395–400.
Dotson, W.G. Jr. On the Mann Iterative Process, Trans. Amer. Math. Soc., 149(1970), 65–73.
Himmelberg, C.J., Measurable Ralations. Fund Math.. LXXXVII(1975), 53–71.
Ishikawa, S., Fixed Points by a New Iteration Method, Proc. Amer, Math. Soc., 44(1974), 147–150.
Maiti, M. and Ghosh, M.K., Approximating Fixed Points by Ishikawa Iterates, Bull. Austral. Math. Soc., 40(1989), 113–117.
Senter, H.F. and Dotson, W.G. Jr., Approximating Fixed Points of Non-Expensive Mappings, Proc. Amer. Math. Soc., 44(1974), 375–380.
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Choudhury, B.S. A random fixed point iteration for three random operators on uniformly convex Banach spaces. Anal. Theory Appl. 19, 99–107 (2003). https://doi.org/10.1007/BF02835233
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DOI: https://doi.org/10.1007/BF02835233