A viscosity projection method for class T mappings

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

xn+1=αnPH(xn, Snxn) f(xn) + (1-αn)Snxn,

where Sn = (1 - w)I + wTn, w ∈ (0; 1); Tn ∈ 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.

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