In this paper we introduce a new algorithm based on the viscosity iteration
method for solving the split common fixed point problem of two infinite
families of k-demicontractive mappings. We shall also study the split common
null point problem, and the split equilibrium problem for this class of
mappings. As an application, we obtain strong convergence theorems for the
split monotone variational inclusion problem and the split variational
inequality problem. Our results improve and extend the recent results of Cui
and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and
Vahidi [17], and many others.
The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.
The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem
