A sufficient condition for the fixed point property

1993 ◽  
Vol 20 (7) ◽  
pp. 849-853 ◽  
Author(s):  
A. Jiménez-Melado ◽  
E. Lloréns-Fuster
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
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 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 On \(\ell_1\)-preduals distant by 1

2018 ◽  
Vol 72 (2) ◽  
pp. 41
Author(s):  
Łukasz Piasecki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Wide Class ◽  
Fixed Point Theory ◽  
General Setting ◽  
Point Theory ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property ◽  
Weak Fixed Point Property

For every predual \(X\) of \(\ell_1\) such that the standard basis in \(\ell_1\) is weak\(^*\) convergent, we give explicit models of all Banach spaces \(Y\) for which the Banach-Mazur distance \(d(X,Y)=1\). As a by-product of our considerations, we obtain some new results in metric fixed point theory. First, we show that the space \(\ell_1\), with a predual \(X\) as above, has the stable weak\(^*\) fixed point property if and only if it has almost stable weak\(^*\) fixed point property, i.e. the dual \(Y^*\) of every Banach space \(Y\) has the weak\(^*\) fixed point property (briefly, \(\sigma(Y^*,Y)\)-FPP) whenever \(d(X,Y)=1\). Then, we construct a predual \(X\) of \(\ell_1\) for which \(\ell_1\) lacks the stable \(\sigma(\ell_1,X)\)-FPP but it has almost stable \(\sigma(\ell_1,X)\)-FPP, which in turn is a strictly stronger property than the \(\sigma(\ell_1,X)\)-FPP. Finally, in the general setting of preduals of \(\ell_1\), we give a sufficient condition for almost stable weak\(^*\) fixed point property in \(\ell_1\) and we prove that for a wide class of spaces this condition is also necessary.

A generalization of the Banach contraction principle in noncomplete metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3357-3363
Author(s):  
Tomonari Suzuki
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Property ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Sufficient Condition ◽  
Point Property ◽  
Banach Contraction ◽  
The Banach Contraction Principle

We give a sufficient condition on metric spaces possessing the Banach fixed point property (BFPP). Further we also give a sufficient condition on not possessing BFPP.

scholarly journals The fixed point property and normal structure for some B-convex Banach spaces

2001 ◽  
Vol 63 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Jesús García-Falset ◽  
Enrique Llorens-Fuster ◽  
Eva M. Mazcuñán-Navarro
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property

We give a sufficient condition for normal structure more general than the well known ɛ0(X) < 1. Moreover we obtain sufficient conditions for the fixed point property for some B-convex Banach spaces.

scholarly journals Brush spaces and the fixed point property

2011 ◽  
Vol 158 (8) ◽  
pp. 1085-1089 ◽  
Author(s):  
M.M. Marsh ◽  
J.R. Prajs
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

scholarly journals A product space with the fixed point property

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Helga Fetter Nathansky ◽  
Enrique Llorens-Fuster
Keyword(s):  
Fixed Point ◽  
Product Space ◽  
Fixed Point Property ◽  
Point Property
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