In this paper, we introduce a viscosity iterative algorithm for finding common solution of variational inequality for Lipschitzian and strongly monotone operators and the split equality common fixed-point problem for firmly quasi-nonexpansive operators. We prove the strong convergence of the proposed algorithm which does not need any prior information about the bounded linear operator norms. c 2016 All rights reserved.Keywords: Split equality problem, firmly quasi-nonexpansive operators, strong convergence, viscosity iterative algorithm, Hilbert space.
In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.
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