#### Dianlu Tian, Lining Jiang, Luoyi Shi, Rudong Chen, Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces, Vol. 2019 (2019), Article ID 11, pp. 1-12

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DOI: 10.23952/jnfa.2019.11

Received September 7, 2018; Accepted February 22, 2019, March 21, 2019

Abstract. Let $H_1$, $H_2$, $H_3$ be three Hilbert spaces. Let $T_1:H_1\rightarrow H_1$ and $T_2:H_2\rightarrow H_2$ be two quasi-nonexpansive operators. Let $A:H_1\rightarrow H_3$ and $B:H_2\rightarrow H_3$ be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find $x\in H_1$ and $y\in H_2$ such that $x=T_1x,$ $y=T_2y$ and $Ax=By$. In this paper, we introduce an iterative algorithm to solve the split equality fixed point problem. We show that the proposed algorithm is strongly convergent without any compactness imposed on the operators.