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In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms. [ABSTRACT FROM AUTHOR]

Let,andbe real Hilbert spaces, letandbe two bounded linear operators. Moudafi introduced simultaneous iterative algorithms with weak convergence for the following split common fixed-point problem:Section.Displaywhereandare two firmly quasi-nonexpansive operators with nonempty fixed-point setsand. Note that, by takingand, we recover the split common fixed-point problem originally introduced by Cesnor and Segal. However, to employ Moudafi’s algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. In this paper, we will continue to consider the split common fixed-point problem (1) governed by the general class of quasi-nonexpansive operators. We introduce a simultaneous iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. The weak convergence result of algorithm is obtained and some applied nonlinear analysis examples are stated. [ABSTRACT FROM AUTHOR]

In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]