The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings (Q1963018)

The so-called ``variational inclusion problem'' VIP \((T,A,g,\Phi)\) in a Banach space is the following: for any \(f\in X\) to find an \(u\in X\) such that \(g(u)\in D(\partial\Phi)\), \[ \langle Tu- Au-f, v- g(u)\rangle\geq \Phi(g(u))- \Phi(v), \] for all \(v\in X^*\). (Here \(\partial\Phi\) denotes the subdifferential of \(\Phi\).) The purpose of this paper is to study the existence and uniqueness of solutions and also the convergence problem of Mann-Ishikawa iterative processes for a class of accretive VIP.