ITERATIVE APPROXIMATION OF FIXED POINTS FOR ASYMPTOTICALLY STRICT PSEUDOCONTRACTIVE TYPE MAPPINGS IN THE INTERMEDIATE SENSE

We introduced the concept of an asymptoticallyκ-strict pseudocontractive type mapping in the intermediate sense which is not necessarily Lipschitzian. We proved that the modified Mann iteration process:x n+1= (1 −αn )xn +αnTnxn , ∀n≥ 1 where {αn } is a sequence in (0, 1) withδ≤αn ≤ 1 −κ−δforδ∈ (0, 1...

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Published inTaiwanese journal of mathematics Vol. 15; no. 2; pp. 587 - 606
Main Authors Ceng, Lu-Chuan, Petruşel, Adrian, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2011
Subjects
Approximation
Hilbert spaces
Iterative methods
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Summary:We introduced the concept of an asymptoticallyκ-strict pseudocontractive type mapping in the intermediate sense which is not necessarily Lipschitzian. We proved that the modified Mann iteration process:x n+1= (1 −αn )xn +αnTnxn , ∀n≥ 1 where {αn } is a sequence in (0, 1) withδ≤αn ≤ 1 −κ−δforδ∈ (0, 1) converges weakly to a fixed point of an asymptoticallyκ-strict pseudocontractive type mappingTin the intermediate sense. Furthermore, a CQ method which generates a strongly convergent sequence for this class of mappings is proposed and strong convergence result for this CQ method is established. 2000Mathematics Subject Classification: Primary 47H09; Secondary 46B20, 47H10. Key words and phrases: Demiclosedness principle, Asymptotically nonexpansive mapping, Asymptotically strict pseudocontractive mapping, Metric projection.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406223