A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces

Abstract

Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. 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