Weak convergence of an iterative sequence for accretive operators in Banach spaces

By Koji Aoyama, Hideaki Iiduka, Wataru Takahashi. 2006

140 citations recorded by the source corpus.

Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/021af740c38e41467443e09cbab55524b4b7eaeb

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Citations in the corpus

Weak convergence of a projection algorithm for variational inequalities in a Banach space (2008, background): “On the weak convergence in the Lebesgue spaces L (p 2), see Aoyama, Iiduka and Takahashi [3].”
Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces (2010, methodology): “Several numerical methods have been developed for solving variational inequalities and related optimization problems, see [1–45] and the references therein.”