Research Article | Open | Published:
Weak convergence of an iterative sequence for accretive operators in Banach spaces
Fixed Point Theory and Applicationsvolume 2006, Article number: 35390 (2006)
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.
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