Strong Convergence Of Iterative Algorithms Based On Projection Technique

In this paper,split equality problems,variational inequality problems and common fixed point problems are studied in Hilbert spaces.Some iterative algorithms based on projection technique are constructed to approximate the solutions of these problems.Meanwhile,some numerical examples are given to test the effectiveness of the proposed algorithms.In view of this,this paper is divided into the following parts:1.Introduce the research background of relevant issues and some preparatory knowledge to be used in this paper.2.A new relaxed alternating CQ algorithm for solving the split equality problem(SEP)based on viscosity approximation methods is constructed in Hilbert spaces,and a strong convergence result is established under preset conditions.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.3.In Hilbert spaces,for solving the variational inequality problem with monotone Lipschitz continuity and the common fixed point problem with an infinite family of multivalued demicontractive mappings,a new viscosity inertial subgradient extragradient algorithm is introduced.The strong convergence result of the constructed algorithm is proved under appropriate conditions.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.4.In Hilbert spaces,two new adaptive inertial subgradient extragradient algorithms for solving the variational inequality problem with monotone Lipschitz continuity and common fixed point problem with an infinite family of multivalued demicontractive mappings are constructed.Under appropriate conditions,strong convergence results are obtained.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.5.Summary and prospect.