Strong convergence results for the split common fixed point problem :

He, Huimin¹ ; Liu, Sanyang¹ ; Chen, Rudong² ; Wang, Xiaoyin²

¹ School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
² Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 9, p. 5332-5343

Résumé

Recently, Boikanyo [O. A. Boikanyo, Appl. Math. Comput., 265 (2015), 844-853] constructed an algorithm for demicontractive operators and obtained the strong convergence theorem for the split common fixed point problem. In this paper, we mainly consider the viscosity iteration algorithm of the algorithm Boikanyo to approximate the split common fixed point problem, and we get the generated sequence strongly converges to a solution of this problem. The main results in this paper extend and improve some results of Boikanyo [O. A. Boikanyo, Appl. Math. Comput., 265 (2015), 844-853] and Cui and Wang [H. H. Cui, F. H. Wang, Fixed Point Theory Appl., 2014 (2014), 8 pages]. The research highlights of this paper are novel algorithms and strong convergence results.

Détail

DOI : 10.22436/jnsa.009.09.02

Classification : 47J25
Keywords: Split common fixed point problem, demicontractive mapping, explicit viscosity algorithm, strong convergence.

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