Fixed point property of amenable planar vortexes

This article introduces free group representations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day during the 1960s and a fundamental result for fixed points given by L.E.J. Brouwer.

New examples of subsets of c with the FPP and stability of the FPP in hyperconvex spaces

The 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.

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

It 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.

General Higher-Order Lipschitz Mappings

In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.

The almost fixed point property is not invariant under isometric renormings

In the present note we prove the non set-stability of the AFPP under isometric renormings in the setting of Banach spaces containing a complemented isomorphic copy of $$c_0$$ c 0 or $$\ell _1$$ ℓ 1