Some improvements on weak convergence theorems of Chuang and Takahashi in Hilbert spaces

Chanitnan Jaipranop; Satit Saejung

Authors

Chanitnan Jaipranop
Satit Saejung

Keywords:

fixed point, k-demicontractive mapping, Mann iteration, Ishikawa iteration, extragradient method

Abstract

Chuang and Takahashi [3] recently proved three weak convergence theorems for a family of firmly nonexpansive mappings with generalized parameters. We discuss these three results for a family of $gif.latex?k$ -demicontractive mappings where $gif.latex?k\leq&space;1$ . Obviously, the class of $gif.latex?k$ -demicontractive mappings contains all firmly nonexpansive mappings. The situation $gif.latex?k=1$ is extensively studied by means of the Ishikawa iteration and the extragradient method of Korpelevi $gif.latex?\breve{\text{c}}$ . Some numerical results for $gif.latex?k=1$ are presented and further discussed.

Some improvements on weak convergence theorems of Chuang and Takahashi in Hilbert spaces

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