A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

Abstract

The purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Keywords

• firmly nonexpansive
• hilbert spaces
• maximally monotone mapping
• strong convergence
• zero points
• 47h04
• 47h05
• 47h10
• 47j25