Strong convergence results for the split common fixed point problem

Volume 9, Issue 9, pp 5332--5343 http://dx.doi.org/10.22436/jnsa.009.09.02

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Authors

Huimin He - School of Mathematics and Statistics, Xidian University, Xi'an 710071, China. Sanyang Liu - School of Mathematics and Statistics, Xidian University, Xi'an 710071, China. Rudong Chen - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. Xiaoyin Wang - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.

Abstract

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.

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Keywords

• Split common fixed point problem
• demicontractive mapping
• explicit viscosity algorithm
• strong convergence.

MSC

•  47J25

References

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