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An iterative process for a finite family of pseudocontractive mappings

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Abstract

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [Numer. Funct. Anal. Optim., 22, (2001) 767–773]:

$$ x_n = \alpha _n x_{n - 1} + (1 - \alpha _n )T_n x_n ,n \geqslant 1, $$

and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition α n ∈ (0, b] ⊂ (0, 1).

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Authors and Affiliations

  1. College of Mathematics and Information Science, He’nan Normal University, Xinxiang, 453007, P. R. China

    Yi Sheng Song

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  1. Yi Sheng Song
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Correspondence to Yi Sheng Song.

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This paper was supported by the Chinese National Youth Tianyuan Foundation (10726073)

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Song, Y.S. An iterative process for a finite family of pseudocontractive mappings. Acta. Math. Sin.-English Ser. 25, 293–298 (2009). https://doi.org/10.1007/s10114-008-6447-2

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  • DOI: https://doi.org/10.1007/s10114-008-6447-2

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