Some fixed point theorems for concentrative mappings between locally convex linear topological spaces

1996 ◽  
Vol 27 (12) ◽  
pp. 1437-1446 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Topological Spaces ◽  
Locally Convex

scholarly journals Some fixed-point theorems on locally convex linear topological spaces

1975 ◽  
Vol 13 (2) ◽  
pp. 241-254 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Fixed Point ◽  
Topological Space ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Topological Spaces ◽  
The Family ◽  
Image Position ◽  
Commutative Family ◽  
Locally Convex

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 ∈ F and for each x ∈ X, τ-closure of the setcontains a point of M. Then the family F has a common fixed-point in M.

scholarly journals Common coupled fixed point theorems in $d$-complete topological spaces

2012 ◽  
Vol 3 (2) ◽  
pp. 107-114 ◽  
Author(s):  
K‎. ‎P‎. ‎R‎. ‎Rao ◽  
‎K‎. ‎R‎. ‎K‎. ‎Rao ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Topological Spaces ◽  
Common Coupled Fixed Point

scholarly journals Fixed point theorems for condensing multivalued mappings on a locally convex topological space

1975 ◽  
Vol 12 (2) ◽  
pp. 161-170 ◽  
Author(s):  
E. Tarafdar ◽  
R. Výborný
Keyword(s):  
Fixed Point ◽  
Topological Space ◽  
Fixed Point Theorems ◽  
Linear Topological Space ◽  
General Definition ◽  
Multivalued Mappings ◽  
Locally Convex

A general definition for a measure of nonprecompactness for bounded subsets of a locally convex linear topological space is given. Fixed point theorems for condensing multivalued mappings have been proved. These fixed point theorems are further generalizations of Kakutani's fixed point theorems.

Sign in / Sign up

Export Citation Format

Share Document