Algorithms of common solutions to modified generalized system of variational inclusion problem and hierarchical fixed point problem

Abstract

This manuscript deals with two problems : the first one is  a new problem of the system of variational inclusion that is called modified generalized system of variational inclusion problem(MGSVIP) and the other one is a hierarchical fixed point problem in the framework of real Hilbert space. We establish the important lemma which show associated between fixed point of nonlinear mapping and solution of MGSVIP as a tool for proving the main theorem. To approximate the common solution of these problems, we design  an iterative scheme under suitable conditions on parameters. A strong convergence result for the proposed iterative scheme is proved. Applying our main result, we prove strong convergence theorems of the modification system of variational inequalities problem and variational inclusion problem. Moreover, we give the numerical example for supporting our results.