Some fixed-point theorems on locally convex linear topological spaces

Tarafdar E. (1975) Some fixed-point theorems on locally convex linear topological spaces. Bulletin of the Australian Mathematical Society, 13 2: 241-254. doi:10.1017/S0004972700024436


Author Tarafdar E.
Title Some fixed-point theorems on locally convex linear topological spaces
Journal name Bulletin of the Australian Mathematical Society   Check publisher's open access policy
ISSN 1755-1633
Publication date 1975-01-01
Sub-type Article (original research)
DOI 10.1017/S0004972700024436
Volume 13
Issue 2
Start page 241
End page 254
Total pages 14
Subject 2600 Mathematics
Abstract Let (E, τ) be a locally convex linear Hausdorff topological space. We have proved mainly the following results. (i) Let f be nonexpansive on a nonempty τ-sequentially complete, τ-bounded, and starshaped subset M of E and let (I-f) map τ-bounded and τ-sequentially closed subsets of M into τ-sequentially closed subsets of M. Then f has a fixed-point in M. (ii) Let f be nonexpansive on a nonempty, τ-sequentially compact, and starshaped subset M of E. Then f has a fixed-point in M. (iii) Let (E, τ) be τ-quasi-complete. Let X be a nonempty, τ-bounded, τ-closed, and convex subset of E and M be a τ-compact subset of X. Let F be a commutative family of nonexpansive mappings on X having the property that for some f1 [formula omitted] F and for each x [formula omitted] X, τ-closure of the set [formula omitted] contains a point of M. Then the family F has a common fixed-point in M.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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Created: Tue, 23 Aug 2016, 11:32:53 EST by System User