In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem. The results obtained in this paper generalize and improve the recent ones announced by many others. c 2017 All rights reserved.Keywords: Multiple-set split equality common fixed-point problem, demicontractive mapping, strong convergence. 2010 MSC: 47H09, 47H10, 47J05, 54H25.

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In this paper, we study a split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings, and propose some cyclic iterative schemes. Moreover we prove some strong convergence theorems. The results obtained in this paper generalize and improve the recent ones announced by many others.