Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-24
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Let K be a closed, convex, and nonempty subset of a real q-uniformly smooth Banach space E, which is also uniformly convex.
For some κ>0, let Ti:K→E i∈ℕ and A:K→E be family of nonexpansive maps and κ-inverse strongly accretive map, respectively.
Let G:K×K→ℝ be a bifunction satisfying some conditions.
Let PK be a nonexpansive projection of E onto K.
For some fixed real numbers δ∈(0,1), λ∈(0,(qκ/dq)1/(q-1)), and arbitrary but fixed vectors x1,u∈E, let {xn} and {yn} be sequences generated by G(yn,η)+(1/r)〈η-yn, jq(yn-xn)〉≥0, ∀η∈K, xn+1=αnu+(1-δ)(1-αn)xn+δ∑i≥1σinTiPK(yn-λAyn), n≥1, where r∈(0,1) is fixed, and {αn},{σi,n}⊂(0,1) are sequences satisfying appropriate conditions.
If F:=[∩i=1∞F(Ti)]∩VI(K,A)∩EP(G)≠∅, under some mild conditions, we prove that the sequences {xn} and {yn} converge strongly to some element in F.
American Psychological Association (APA)
Ali, Bashir. 2013. Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems. Journal of Mathematics،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-466618
Modern Language Association (MLA)
Ali, Bashir. Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems. Journal of Mathematics No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-466618
American Medical Association (AMA)
Ali, Bashir. Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems. Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-466618
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-466618