<abstract xmlns="http://www.w3.org/1999/xhtml"> 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. </abstract>

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.

A viscosity projection method for class T mappings

College of Science, Civil Aviation University of China, Jinbei Road 2898, 300300, Tianjin, China

Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Jinbei Road 2898, 300300, Tianjin, China

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"A viscosity projection method for class T mappings"}

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...

A viscosity projection method for class T mappings

Published Online: Sep 19, 2013

Page range: 95 - 109

DOI: https://doi.org/10.2478/auom-2013-0025

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