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Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-20
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
Let C be a nonempty bounded closed convex subset of a complete CAT(0) space X.
We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex.
We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmk)xk⊕tmkTmnky(m-1)k, y(m-1)k=(1-t(m-1)k)xk⊕t(m-1)kTm-1nky(m-2)k,y(m-2)k=(1-t(m-2)k)xk⊕t(m-2)kTm-2nky(m-3)k,…,y2k=(1-t2k)xk⊕t2kT2nky1k,y1k=(1-t1k)xk⊕t1kT1nky0k,y0k=xk, k∈ℕ, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers.
The related results for uniformly convex Banach spaces are also included.
American Psychological Association (APA)
Pasom, P.& Panyanak, B.. 2012. Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-993155
Modern Language Association (MLA)
Pasom, P.& Panyanak, B.. Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces. Journal of Applied Mathematics No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-993155
American Medical Association (AMA)
Pasom, P.& Panyanak, B.. Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-993155
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993155