Abstract
Let K be a closed convex subset of a real Hilbert space H and let T:K→K be a continuous pseudocontractive mapping. Then for βε(0,1) and each tε(0,1), there exists a sequence { yt}⊂K satisfying yt=βPK[(1-t)yt]+(1-β)T(yt) which converges strongly, as t→0+, to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.
| Original language | English |
|---|---|
| Article number | 926017 |
| Journal | Abstract and Applied Analysis |
| Volume | 2012 |
| DOIs | |
| Publication status | Published - Dec 1 2012 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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Minimum-norm fixed point of pseudocontractive mappings. / Zegeye, Habtu; Shahzad, Naseer; Alghamdi, Mohammad Ali.
In: Abstract and Applied Analysis, Vol. 2012, 926017, 01.12.2012.Research output: Contribution to journal › Article
TY - JOUR
T1 - Minimum-norm fixed point of pseudocontractive mappings
AU - Zegeye, Habtu
AU - Shahzad, Naseer
AU - Alghamdi, Mohammad Ali
PY - 2012/12/1
Y1 - 2012/12/1
N2 - Let K be a closed convex subset of a real Hilbert space H and let T:K→K be a continuous pseudocontractive mapping. Then for βε(0,1) and each tε(0,1), there exists a sequence { yt}⊂K satisfying yt=βPK[(1-t)yt]+(1-β)T(yt) which converges strongly, as t→0+, to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.
AB - Let K be a closed convex subset of a real Hilbert space H and let T:K→K be a continuous pseudocontractive mapping. Then for βε(0,1) and each tε(0,1), there exists a sequence { yt}⊂K satisfying yt=βPK[(1-t)yt]+(1-β)T(yt) which converges strongly, as t→0+, to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.
UR - http://www.scopus.com/inward/record.url?scp=84874915810&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874915810&partnerID=8YFLogxK
U2 - 10.1155/2012/926017
DO - 10.1155/2012/926017
M3 - Article
AN - SCOPUS:84874915810
VL - 2012
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
SN - 1085-3375
M1 - 926017
ER -