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

Abstract

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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Correspondence to Hideaki Iiduka.

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Aoyama, K., Iiduka, H. & Takahashi, W. Weak convergence of an iterative sequence for accretive operators in Banach spaces. Fixed Point Theory Appl 2006, 35390 (2006). https://doi.org/10.1155/FPTA/2006/35390

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Keywords

  • Banach Space
  • Differential Geometry
  • Weak Convergence
  • Computational Biology
  • Iterative Sequence
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