Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.