We investigate the following regularized gradient projection algorithmxn+1=Pc(I−γn(∇f+αnI))xn,n≥0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problemminx∈Cf(x).

We First introduce a three-step iterative algorithm for approximating the fixed points of the hemicontractive mappings in Banach spaces. Consequently, we prove the strong convergence of the proposed algorithm under some assumptions. Since three-step iterations include Ishikawa iterations as special cases, our result continue to hold for these problems. Our main results can be viewed as an important refinement of the previously known results.

A general hierarchical problem has been considered, and an explicit algorithm has been presented for solving this hierarchical problem. Also, it is shown that the suggested algorithm converges strongly to a solution of the hierarchical problem.

a b s t r a c tThe split feasibility problem models inverse problems arising from phase retrieval problems and the intensity modulated radiation therapy. In this paper, two methods have been presented for solving the split feasibility problem. The strong convergence results of presented algorithms have been obtained under some mild conditions. Especially, the minimum norm solution of the split feasibility problem can be found.

Two hybrid algorithms for the variational inequalities over the common fixed points set of nonexpansive semigroups are presented. Strong convergence results of these two hybrid algorithms have been obtained in Hilbert spaces. The results improve and extend some corresponding results in the literature.