Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem

Xia Li; Meifang Guo; Yongfu Su

doi:10.1186/s40064-016-3691-2

Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem

Springerplus. 2016 Nov 24;5(1):2009. doi: 10.1186/s40064-016-3691-2. eCollection 2016.

Authors

Xia Li¹, Meifang Guo¹, Yongfu Su²

Affiliations

¹ Deprtment of Mathematics and Sciences, Hebei GEO University, Shijiazhuang, 050031 China.
² Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387 China.

Abstract

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. Strong convergence theorems for finding a solution of the split common null point problem are derived. This iteration algorithm can accelerate the convergence speed of iterative sequence. The results of this paper improve and extend the recent results of Takahashi and Yao (Fixed Point Theory Appl 2015:87, 2015) and many others .

Keywords: Duality mapping; Fixed point; Metric resolvent; Multidirectional hybrid algorithm; Split common fixed point problem; Split common null point problem.