A viscosity projection method for class T mappings

In this paper, we firstly introduce a viscosity projection method for the class T mappings

x_n+1=α_nP_H(x_n, S_nx_n) f(x_n) + (1-α_n)S_nx_n,

where S_n = (1 - w)I + wT_n, w ∈ (0; 1); T_n ∈ T and prove strong convergence theorems of the proposed method. It is verified that the viscosity projection method converges locally faster than the viscosity method. Furthermore, we present a viscosity projection method for a quasi-nonexpansive and nonexpansive mappings in Hilbert spaces. A numerical test provided in the paper shows that the viscosity projection method converges faster than the viscosity method.