A Strong Convergence Theorem under a New Shrinking Projection Method for Finite Families of Nonlinear Mappings in a Hilbert Space

Abstract

In this paper, using a new shrinking projection method, we deal with the strong convergence for finding a common point of the sets of zero points of a maximal monotone mapping, common fixed points of a finite family of demimetric mappings and common zero points of a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we get well-known and new strong convergence theorems in a Hilbert space.

Keywords

• fixed point
• demimetric mapping
• inverse strongly monotone mapping
• maximal monotone mapping
• shrinking projection method
• variational inequality problem