scholarly journals A 3-space problem related to the fixed point property

2001 ◽  
Vol 64 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Helga Fetter ◽  
Berta Gamboa de Buen
Keyword(s):  
Fixed Point ◽  
Dimensional Space ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Finite Dimensional Space ◽  
Point Property ◽  
Space Problem ◽  
Opial’S Condition ◽  
Direct Sum ◽  
Finite Dimensional

We study some properties which imply weak normal structure and thus the fixed point property. We investigate whether the latter two properties are inherited by spaces obtained by direct sum with a finite dimensional space. We exhibit a space X which satisfies Opial's condition, X ⊕ ℝ does not have weak normal structure but X ⊕ ℝ has the fixed point property.

scholarly journals On the modulus ofu-convexity of Ji Gao

2003 ◽  
Vol 2003 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Eva María Mazcuñán-Navarro
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property

We consider the modulus ofu-convexity of a Banach space introduced by Ji Gao (1996) and we improve a sufficient condition for the fixed-point property (FPP) given by this author. We also give a sufficient condition for normal structure in terms of the modulus ofu-convexity.

scholarly journals A class of spaces with weak normal structure

1994 ◽  
Vol 49 (3) ◽  
pp. 523-528 ◽  
Author(s):  
Brailey Sims
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Point Property ◽  
Weak Fixed Point Property

It has recently been shown that a Banach space enjoys the weak fixed point property if it is ε0-inquadrate for some ε0 < 2 and has WORTH; that is, if then, ║xn — x║ — ║xn + x║ → 0, for all x. We establish the stronger conclusion of weak normal structure under the substantially weaker assumption that the space has WORTH and is ‘ε0-inquadrate in every direction’ for some ε0 < 2.

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 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.

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