Affiliation:
1. Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
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 that show the relation between fixed point of
nonlinear mapping and solution of MGSVIP 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.
Publisher
National Library of Serbia