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Faculty of Sciences
Document Details
Document Type
:
Article In Journal
Document Title
:
Viscosity approximation methods for pseudocontractive mappings in Banach spaces
Viscosity approximation methods for pseudocontractive mappings in Banach spaces
Subject
:
Mathematics
Document Language
:
English
Abstract
:
Let K be a closed convex subset of a Banach space E and let T : K → E be a continuous weakly inward pseudocontractive mapping. Then for t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = (1 - t)f(yt) + tT(yt), where f ∈ ΠK {colon equals} {f : K → K, a contraction with a suitable contractive constant}. Suppose further that F(T) ≠ ∅ and E is reflexive and strictly convex which has uniformly Gâteaux differentiable norm. Then it is proved that {yt} converges strongly to a fixed point of T which is also a solution of certain variational inequality. Moreover, an explicit iteration process which converges strongly to a fixed point of T and hence to a solution of certain variational inequality is constructed provided that T is Lipschitzian.
ISSN
:
0096-3003
Journal Name
:
Applied Mathematics and Computation
Volume
:
185
Issue Number
:
1
Publishing Year
:
1428 AH
2007 AD
Article Type
:
Article
Added Date
:
Saturday, December 17, 2011
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
H Zegeye
Zegeye, H
Researcher
Master
habtuzh@yahoo.com
نصير شهزاد
Shahzad, Naseer
Researcher
Doctorate
nshahzad@kau.edu.sa
Tefera Mekonen
Mekonen, Tefera
Researcher
Doctorate
Files
File Name
Type
Description
31682.pdf
pdf
Abstract
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