Banach spaces which are somewhat uniformly noncreasy (original) (raw)
Nearly uniformly noncreasy Banach spaces
Journal of Mathematical Analysis and Applications, 2005
We introduce and study the class of nearly uniformly noncreasy Banach spaces. It is proved that they have the weak fixed point property. A stability result for this property is obtained.
International Journal of Pure and Applied Mathematics
In this paper, the properties of noncreasy and local uniformly noncreasy are investigated.
New families of nonreflexive Banach spaces with the fixed point property
Journal of Mathematical Analysis and Applications, 2015
In this paper we define the concept of sequentially separating norm and we relate it to the fulfillment of the fixed point property for non-expansive mappings. We develop a technique to construct families of nonreflexive Banach spaces with the fixed point property. Different examples will be exhibited. We also study the geometry of the Banach spaces that can be renormed with a sequentially separating norm.
Common fixed-point results in uniformly convex Banach spaces
Fixed Point Theory and Applications, 2012
We introduce a condition on mappings, namely condition (K). In a uniformly convex Banach space, the condition is weaker than quasi-nonexpansiveness and weaker than asymptotic nonexpansiveness. We also present the existence theorem of common fixed points for a commuting pair consisting of a mapping satisfying condition (K) and a multivalued mapping satisfying conditions (E) and (C λ ) for some λ ∈ (0, 1).
The fixed-point property in Banach spaces containing a copy ofc0
Abstract and Applied Analysis, 2003
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.
Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings
Journal of Functional Analysis, 2006
It is shown that if the modulus X of nearly uniform smoothness of a reflexive Banach space satisfies X (0) < 1, then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.
A renorming in some Banach spaces with applications to fixed point theory
Journal of Functional Analysis, 2010
We consider a Banach space X endowed with a linear topology τ and a family of seminorms {R k (•)} which satisfy some special conditions. We define an equivalent norm ||| • ||| on X such that if C is a convex bounded closed subset of (X, ||| • |||) which is τ -relatively sequentially compact, then every nonexpansive mapping T : C → C has a fixed point. As a consequence, we prove that, if G is a separable compact group, its Fourier-Stieltjes algebra B(G) can be renormed to satisfy the FPP. In case that G = T, we recover P.K. Lin's renorming in the sequence space 1 . Moreover, we give new norms in 1 with the FPP, we find new classes of nonreflexive Banach spaces with the FPP and we give a sufficient condition so that a nonreflexive subspace of L 1 (μ) can be renormed to have the FPP.
Fixed Point in Modified Semi-linear Uniform Spaces
2017
Tallafha, A. andAlhihi, S. in [17], Defined m−contraction, and modefid semi-linear uniform space (X, ), and asked the following question. If f is an m−contraction from a complete modified semi-linear uniform space (X, ) to it self, is f has a unique fixed point. In this paper we shall answer partially the question given by Tallafha, A. and Alhihi, S. in [17] for 2−contraction, besides we shall give an intrested properties of modefied semi-linear uniform spaces. AMS subject classification: Primary 54E35, Secondary 41A65.