A fixed-point characterization of weakly compact sets in L1(μ) spaces

2020 ◽  
Vol 491 (1) ◽  
pp. 124228
Author(s):  
Maria Japón ◽  
Chris Lennard ◽  
Roxana Popescu
Keyword(s):  
Fixed Point ◽  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 373-387 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Compact Sets ◽  
Multivalued Maps ◽  
Weakly Compact ◽  
Topological Vector Spaces ◽  
Admissible Maps ◽  
Weakly Compact Sets ◽  
Locally Convex

We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

scholarly journals New examples of subsets of c with the FPP and stability of the FPP in hyperconvex spaces

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Rafael Espínola-García ◽  
María Japón ◽  
Daniel Souza
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Point Property ◽  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets ◽  
The One

AbstractThe purpose of this work is two-fold. On the one side, we focus on the space of real convergent sequences c where we study non-weakly compact sets with the fixed point property. Our approach brings a positive answer to a recent question raised by Gallagher et al. in (J Math Anal Appl 431(1):471–481, 2015). On the other side, we introduce a new metric structure closely related to the notion of relative uniform normal structure, for which we show that it implies the fixed point property under adequate conditions. This will provide some stability fixed point results in the context of hyperconvex metric spaces. As a particular case, we will prove that the set $$M=[-1,1]^\mathbb {N}$$ M = [ - 1 , 1 ] N has the fixed point property for d-nonexpansive mappings where $$d(\cdot ,\cdot )$$ d ( · , · ) is a metric verifying certain restrictions. Applications to some Nakano-type norms are also given.

scholarly journals Characterizations of weakly compact sets and new fixed point free maps in c0

2003 ◽  
Vol 154 (3) ◽  
pp. 277-293 ◽  
Author(s):  
P. N. Dowling ◽  
C. J. Lennard ◽  
B. Turett
Keyword(s):  
Fixed Point ◽  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

A Weak Hadamard Smooth Renorming of L1(Ω, μ)

1993 ◽  
Vol 36 (4) ◽  
pp. 407-413 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Simon Fitzpatrick
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

AbstractWe show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.

Weakly compact sets in L∞(μ,E)

2012 ◽  
Vol 263 (4) ◽  
pp. 1098-1102
Author(s):  
Surjit Singh Khurana
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

Weakly compact sets in Orlicz sequence spaces

2021 ◽  
pp. 1-14
Author(s):  
Siyu Shi ◽  
Zhongrui Shi ◽  
Shujun Wu
Keyword(s):  
Sequence Spaces ◽  
Compact Sets ◽  
Weakly Compact ◽  
Orlicz Sequence Spaces ◽  
Weakly Compact Sets

Banach Spaces that are Uniformly Rotund in Weakly Compact Sets of Directions

1977 ◽  
Vol 29 (5) ◽  
pp. 963-970 ◽  
Author(s):  
Mark A. Smith
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Nonzero Element ◽  
Bounded Subset ◽  
Compact Sets ◽  
Weakly Compact ◽  
Uniform Rotundity ◽  
Minimum Depth ◽  
Weakly Compact Sets

In a Banach space, the directional modulus of rotundity, δ (ϵ, z), measures the minimum depth at which the midpoints of all chords of the unit ball which are parallel to z and of length at least ϵ are buried beneath the surface. A Banach space is uniformly rotund in every direction (URED) if δ (ϵ, z) is positive for every positive ϵ and every nonzero element z. This concept of directionalized uniform rotundity was introduced by Garkavi [6] to characterize those Banach spaces in which every bounded subset has at most one Čebyšev center.

Sign in / Sign up

Export Citation Format

Share Document