Asymptotic centers in 𝑐₀, 𝑐 and π‘š

1983 β—½  
pp. 141-154 β—½  
Author(s):  
Teck-Cheong Lim
Keyword(s):  
Asymptotic Centers

On Asymptotic Centers and Fixed Points of Nonexpansive Mappings

1980 β—½  
Vol 32 (2) β—½  
pp. 421-430 β—½  
Author(s):  
Teck-Cheong Lim
Keyword(s):  
Banach Space β—½  
Fixed Points β—½  
Nonempty Subset β—½  
Nonexpansive Mappings β—½  
Chebyshev Center β—½  
Bounded Subset β—½  
Uniformly Convex β—½  
Weakly Compact β—½  
Asymptotic Centers β—½  
Image Position

Let X be a Banach space and B a bounded subset of X. For each x ∈ X, define R(x) = sup{β€–x – yβ€– : y ∈ B}. If C is a nonempty subset of X, we call the number R = inΖ’{R(x) : x ∈ C} the Chebyshev radius of B in C and the set the Chebyshev center of B in C. It is well known that if C is weakly compact and convex, then and if, in addition, X is uniformly convex, then the Chebyshev center is unique; see e.g., [9].Let {BΞ± : Ξ± ∈ ∧} be a decreasing net of bounded subsets of X. For each x ∈ X and each Ξ± ∈ ∧, define

scholarly journals Remarks on Asymptotic Centers and Fixed Points

2010 β—½  
Vol 2010 β—½  
pp. 1-5
Author(s):  
A. Kaewkhao β—½  
K. Sokhuma
Keyword(s):  
Banach Space β—½  
Convex Subset β—½  
Compact Convex β—½  
Bounded Sequence β—½  
Point Property β—½  
Weakly Compact β—½  
Asymptotic Center β—½  
Continuous Mappings β—½  
Weak Fixed Point Property β—½  
Asymptotic Centers

We introduce a class of nonlinear continuous mappings defined on a bounded closed convex subset of a Banach spaceX. We characterize the Banach spaces in which every asymptotic center of each bounded sequence in any weakly compact convex subset is compact as those spaces having the weak fixed point property for this type of mappings.

scholarly journals An explicit iteration for asymptotic centers of orbits of nonexpansive mappings in Banach spaces

1989 β—½  
Vol 57 (1) β—½  
pp. 40-47 β—½  
Author(s):  
Norimichi Hirano β—½  
Kazuo Kido β—½  
Wataru Takahashi
Keyword(s):  
Banach Spaces β—½  
Nonexpansive Mappings β—½  
Asymptotic Centers

scholarly journals Fixed Point Theorems by Ways of Ultra-Asymptotic Centers

2011 β—½  
Vol 2011 β—½  
pp. 1-21 β—½  
Author(s):  
S. Dhompongsa β—½  
N. Nanan
Keyword(s):  
Fixed Point β—½  
Fixed Point Theorems β—½  
Multivalued Mappings β—½  
Asymptotic Centers

We use an approach on ultra-asymptotic centers to obtain fixed point theorems for two classes of nonself multivalued mappings. The results extend and improve several known ones.

Sign in / Sign up

Export Citation Format

Share Document