  In this paper we propose new averaged iterative algorithms designed for
solving a split common fixed-point problem in the class of demicontractive
mappings. The algorithms are obtained by inserting an averaged term into the
algorithms used in [Li, R. and He, Z., A new iterative algorithm for split
solution problems of quasi-nonexpansive mappings {\it J. Inequal. Appl.} {\bf
131} (2015), 1--12.] for solving the same problem but in the class of
quasi-nonexpansive mappings, which is a subclass of demicontractive mappings.
Basically, our investigation is based on the embedding of demicontractive
operators in the class of quasi-nonexpansive operators by means of averaged
mappings. For the considered algorithms we prove weak and strong convergence
theorems in the setting of a real Hilbert space and also provide examples to
show that our results are effective generalizations of existing results in
literature.
