doi:10.1016/j.na.2008.02.092 
Copyright © 2008 Elsevier Ltd All rights reserved.
Strong and weak convergence theorems for nonself-asymptotically perturbed nonexpansive mappings
aSchool of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C. G.) 492010, India
bDepartment of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
cDepartment of Mathematics and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
Received 30 January 2008;
accepted 22 February 2008.
Available online 29 February 2008.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
Suppose that K1 and K2 are nonempty closed convex subsets of a real uniformly convex Banach space E which are also nonexpansive retracts of E with retractions P and Q, respectively. Let T1:K1→E and T2:K2→E be two nonself asymptotically perturbed P-nonexpansive and Q-nonexpansive mappings satisfying the ball condition with sequences {kn}, {ln}
[1−
,∞), limn→∞kn=1−, limn→∞ln=1−, F(T1)∩F(T2)={x
K1∩K2:T1x=T2x=x}≠0/, respectively, such that K2
(1−λ)K1+λT1(K1) for each λ[,1−) for some >0. Suppose that {xn} is generated iteratively by
for each
n≥1, where
{αn} and
{βn} are two real sequences in
[,1−) for some
>0. (1) If one of
T1 and
T2 is completely continuous or demicompact and
,
, where
and
, then strong convergence theorems of both
{xn} and
{yn} to some
qF(T1)∩F(T2) are obtained. (2) If
E is real uniformly convex Banach space satisfying Opial’s condition, then weak convergence of both
{xn} and
{yn} to some
qF(T1)∩F(T2) are obtained.
Keywords: Strong and weak convergence; Nonself asymptotically mapping; Nonself asymptotically perturbed mapping; Common fixed point
Mathematical subject codes: 54H25; 47H10; 54C60
|
Note to users: The section "Articles in Press" contains peer reviewed accepted articles to be published in this journal. When the final article is assigned to an issue of the journal, the "Article in Press" version will be removed from this section and will appear in the associated published journal issue. The date it was first made available online will be carried over. Please be aware that although "Articles in Press" do not have all bibliographic details available yet, they can already be cited using the year of online publication and the DOI as follows: Author(s), Article Title, Journal (Year), DOI. Please consult the journal's reference style for the exact appearance of these elements, abbreviation of journal names and the use of punctuation.
|
| There are three types of "Articles in Press": |
- Accepted manuscripts: these are articles that have been peer reviewed and accepted for publication by the Editorial Board. The articles have not yet been copy edited and/or formatted in the journal house style.
- Uncorrected proofs: these are copy edited and formatted articles that are not yet finalized and that will be corrected by the authors. Therefore the text could change before final publication.
- Corrected proofs: these are articles containing the authors' corrections and may, or may not yet have specific issue and page numbers assigned.
|
Abstract
Purchase PDF (290 K)
E-mail Article
Add to my Quick Links
Purchase PDF (275 K)
