The fixed point property under renorming in some classes of Banach spaces

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1409-1416 ◽  
Author(s):  
T. Domínguez Benavides ◽  
S. Phothi
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Property ◽  
Point Property

The fixed point property for some uniformly nonoctahedral Banach spaces

1999 ◽  
Vol 59 (3) ◽  
pp. 361-367 ◽  
Author(s):  
A. Jiménez-Melado
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Unit Sphere ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property

Roughly speaking, we show that a Banach space X has the fixed point property for nonexpansive mappings whenever X has the WORTH property and the unit sphere of X does not contain a triangle with sides of length larger than 2.

scholarly journals THE FIXED POINT PROPERTY AND UNBOUNDED SETS IN BANACH SPACES

2010 ◽  
Vol 14 (2) ◽  
pp. 733-742 ◽  
Author(s):  
Wataru Takahashi ◽  
Jen-Chih Yao ◽  
Fumiaki Kohsaka
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Normal structure and fixed point property

1996 ◽  
Vol 38 (1) ◽  
pp. 29-37 ◽  
Author(s):  
J. García-Falset ◽  
E. Lloréns-Fuster
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property ◽  
Positive Results

The most classical sufficient condition for the fixed point property of non-expansive mappings FPP in Banach spaces is the normal structure (see [6] and [10]). (See definitions below). Although the normal structure is preserved under finite lp-product of Banach spaces, (1<p≤∞), (see Landes, [12], [13]), not too many positive results are known about the normal structure of an l1,-product of two Banach spaces with this property. In fact, this question was explicitly raised by T. Landes [12], and M. A. Khamsi [9] and T. Domíinguez Benavides [1] proved partial affirmative answers. Here we give wider conditions yielding normal structure for the product X1⊗1X2.

scholarly journals The fixed-point property in Banach spaces containing a copy ofc0

2003 ◽  
Vol 2003 (3) ◽  
pp. 183-192
Author(s):  
Maria A. Japón Pineda
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Weak Topology ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Asymptotically Nonexpansive ◽  
Locally Convex Topology ◽  
Locally Convex

We prove that every Banach space containing an isomorphic copy ofc0fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy ofc0is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.

Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm

2021 ◽  
Author(s):  
Yunan Cui ◽  
Li Zhao
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Orlicz Function ◽  
Function Spaces ◽  
Fixed Point Property ◽  
Point Property ◽  
Orlicz Norm

AbstractIt is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

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