The split common fixed point problem for multivalued demicontractive mappings and its applications

Abstract

© 2018, Springer-Verlag Italia S.r.l., part of Springer Nature. In this article, we consider the split common fixed point problem for two infinite families of multivalued mappings in real Hilbert spaces. We introduce an algorithm based on the viscosity method for solving the split common fixed point problem for two infinite families of multivalued demicontractive mappings. We establish a strong convergence result under some suitable conditions. As applications, we also apply our main result to the split variational inequality problem and the split common null point problem. Finally, we give the numerical example for supporting our main theorem.