Weak Convergence of an Iterative Sequence for Accretive Operators in Banach Spaces

@inproceedings{Aoyama2006WeakCO,
  title={Weak Convergence of an Iterative Sequence for Accretive Operators in Banach Spaces},
  author={Koji Aoyama and Hideaki Iiduka and Akira Takahashi},
  year={2006}
}
Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a… CONTINUE READING