title: Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem.
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 .
authors.affiliation: Deprtment of Mathematics and Sciences, Hebei GEO University, Shijiazhuang, 050031 China.
authors.forename: Xia
authors.initials: X
authors.lastname: Li
authors.affiliation: Deprtment of Mathematics and Sciences, Hebei GEO University, Shijiazhuang, 050031 China.
authors.forename: Meifang
authors.initials: M
authors.lastname: Guo
authors.affiliation: Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387 China.
authors.forename: Yongfu
authors.identifier: 0000-0001-8656-471X
authors.initials: Y
authors.lastname: Su
keywords: Duality mapping; Fixed point; Metric resolvent; Multidirectional hybrid algorithm; Split common fixed point problem; Split common null point problem