Strong Convergence of Iterative Algorithm for a New System of Generalized H · , · - η - Cocoercive Operator Inclusions in Banach Spaces

Abstract

We introduce and study a new system of generalized $H\left(·,·\right)-\eta \text{-}$cocoercive operator inclusions in Banach spaces. Using the resolvent operator technique associated with $H\left(·,·\right)-\eta \text{-}$cocoercive operators, we suggest and analyze a new generalized algorithm of nonlinear set-valued variational inclusions and establish strong convergence of iterative sequences produced by the method. We highlight the applicability of our results by examples in function spaces.