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Let,,be real Hilbert spaces, let,be two bounded linear operators. The multiple-set split equality common fixed-point problem (MSECFP) under consideration in this paper is to(Section.Display) whereare integers,andare quasi-nonexpansive mappings with nonempty fixed-point sets. Note that, the above problem (1) allows asymmetric and partial relations between the variablesand. Ifand, then the MSECFP (1) reduces to the multiple-set split common fixed-point problem proposed by Censor et al. In this paper, we introduce mixed cyclic and simultaneous iterative algorithms for the MSECFP (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. Weak convergence results are given. [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]