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Asymptotically strict pseudocontractive mappings in the intermediate sense

Authors :
Jen-Chih Yao
Hong-Kun Xu
Daya Ram Sahu
Source :
Nonlinear Analysis: Theory, Methods & Applications. 70:3502-3511
Publication Year :
2009
Publisher :
Elsevier BV, 2009.

Abstract

It is proved that the modified Mann iteration process: x n + 1 = ( 1 − α n ) x n + α n T n x n , n ∈ N , where { α n } is a sequence in (0, 1) with δ ≤ α n ≤ 1 − κ − δ for some δ ∈ ( 0 , 1 ) , converges weakly to a fixed point of an asymptotically κ -strict pseudocontractive mapping T in the intermediate sense which is not necessarily Lipschitzian. We also develop CQ method for this modified Mann iteration process which generates a strongly convergent sequence.

Details

ISSN :
0362546X
Volume :
70
Database :
OpenAIRE
Journal :
Nonlinear Analysis: Theory, Methods & Applications
Accession number :
edsair.doi...........9c01a041b420b62ae2fb0a59eee0a4ba
Full Text :
https://doi.org/10.1016/j.na.2008.07.007