Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-16
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Let A and B be two nonempty subsets of a Banach space X.
A mapping T : A ∪ B → A ∪ B is said to be cyclic relatively nonexpansive if T(A) ⊆ B and T(B) ⊆ A and T x - T y ≤ x - y for all ( x , y ) ∈ A × B .
In this paper, we introduce a geometric notion of seminormal structure on a nonempty, bounded, closed, and convex pair of subsets of a Banach space X.
It is shown that if (A, B) is a nonempty, weakly compact, and convex pair and (A, B) has seminormal structure, then a cyclic relatively nonexpansive mapping T : A ∪ B → A ∪ B has a fixed point.
We also discuss stability of fixed points by using the geometric notion of seminormal structure.
In the last section, we discuss sufficient conditions which ensure the existence of best proximity points for cyclic contractive type mappings.
American Psychological Association (APA)
Gabeleh, Moosa& Shahzad, Naseer. 2014. Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013297
Modern Language Association (MLA)
Gabeleh, Moosa& Shahzad, Naseer. Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1013297
American Medical Association (AMA)
Gabeleh, Moosa& Shahzad, Naseer. Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013297
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013297