Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings

Esref Turkmen, Safeer Hussain Khan and Murat Ozdemir

Discrete Dynamics in Nature and Society, 2011, vol. 2011, 1-16

Abstract:

Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F : = F ( T 1 ) ∩ F ( T 2 ) = { x ∈ K : T 1 x = T 2 x = x } ≠ ∅ . Let T 1 , T 2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences { k n ( i ) } ⊂ [ 1 , ∞ ) satisfying ∑ n = 1 ∞ ( k n ( i ) - 1 ) < ∞ ( i = 1,2 ) , respectively. For any given x 1 ∈ K , suppose that { x n } is a sequence generated iteratively by x n + 1 = ( 1 - α n ) ( P T 1 ) n y n + α n ( P T 2 ) n y n , y n = ( 1 - β n ) x n + β n ( P T 1 ) n x n , n ∈ N , where { α n } and { β n } are sequences in [ a , 1 - a ] for some a ∈ ( 0,1 ) . Under some suitable conditions, the strong and weak convergence theorems of { x n } to a common fixed point of T 1 and T 2 are obtained.

Date: 2011
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2011/487864.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2011/487864.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:487864

DOI: 10.1155/2011/487864

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().