A novel iterative algorithm with convergence analysis for split common fixed points and variational inequality problems

摘要

We propose a new algorithm which can be considered as a combination between the subgradient extragradient method and viscosity methods for solving split common fixed points problem and variational inequality problem. We find a point which belongs to the set of common fixed points of a finite family of demimetric mappings and the common solutions to a system of variational inequalities problem for a family of monotone and Lipschitz continuous operators in a Hilbert space such that its image under a linear transformation belongs to the set of common fixed points of a finite family of demimetric mappings in uniformly convex and smooth Banach space in the image space. The strong convergence of the sequences generated by the algorithm is proved. We also give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view.