Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-12-03
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, ℱ={T(h):h≥0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f:K→K a fixed contractive mapping with contractive coefficient β∈(0,1).
We prove that the following implicit and modified implicit viscosity iterative schemes {xn} defined by xn=αnf(xn)+(1−αn)T(tn)xn and xn=αnyn+(1−αn)T(tn)xn, yn=βnf(xn−1)+(1−βn)xn−1 strongly converge to p∈F as n→∞ and p is the unique solution to the following variational inequality: 〈f(p)−p,j(y−p)〉≤0 for all y∈F.
American Psychological Association (APA)
Li, Yali& Liu, Jianjun& Deng, Lei. 2008. Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-10.
https://search.emarefa.net/detail/BIM-490670
Modern Language Association (MLA)
Li, Yali…[et al.]. Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-10.
https://search.emarefa.net/detail/BIM-490670
American Medical Association (AMA)
Li, Yali& Liu, Jianjun& Deng, Lei. Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces. International Journal of Mathematics and Mathematical Sciences. 2008. Vol. 2008, no. 2008, pp.1-10.
https://search.emarefa.net/detail/BIM-490670
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490670