Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators

Abstract

Abstract In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method.

Keywords

• hybrid projection methods
• shrinking projection methods
• monotone operators and resolvent