Viscosity Approximation Methods for Split Common Fixed-Point Problem of Directed Operators
Jing Zhao, Songnian He · Numerical Functional Analysis and Optimization · 2015
Let H 1, H 2, H 3 be real Hilbert spaces, let A: H 1 → H 3, B: H 2 → H 3 be two bounded linear operators. The split common fixed-point problem (SCFP) is where U: H 1 → H 1 and T: H 2 → H 2 are two nonlinear operators with nonempty fixed-point sets F(U) = {x ∈ H 1: Ux = x} and F(T) = {x ∈ H 2: Tx = x}. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SCFP (1) of firmly quasi-nonexpansive operators. In this article, we introduce viscosity iterative algorithm and prove the strong convergence of algorithm for the SCFP (1) governed by the directed operators (i.e. firmly quasi-nonexpansive operators). Finally, we provide some applications.