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.

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.

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