Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces

Let H₁,H₂,H₃ be three Hilbert spaces. Let T₁ : H₁ → H₁ and T₂ : H₂ → H₂ be two quasi-nonexpansive operators. Let A : H₁ → H₃ and B : H₂ → H₃ be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find x ∈ H₁ and y ∈ H₂ such that x = T₁x, y = T₂y 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.