Banach spaces which are somewhat uniformly noncreasy

We consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.     

Fixed point theory for a class of generalized nonexpansive mappings

In this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.     

Existence theorems for m-accretive operators in Banach spaces

In 1985, the second author proved a surjective result for m-accretive and ?-expansive mappings for uniformly smooth Banach spaces. However, in this case, we have been able to remove the uniform smoothness of the Banach space, without any additional assumption.     

The asymptotic behavior of the solutions of the Cauchy problem generated by -accretive operators

The purpose of this paper is to study the asymptotic behavior of the solutions of certain type of differential inclusions posed in Banach spaces. In particular, we obtain the abstract result on the asymptotic behavior of the solution of the boundary value problem

where Ω is a bounded open domain in with smooth boundary ∂Ω, f(t,x) is a given L¹-function on ]0,∞[×Ω, γ1 and 1p<∞. Δ_p represents the p-Laplacian operator, is the associated Neumann boundary operator and β a maximal monotone graph in with 0β(0).     

Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

It is shown that if the modulus Γ_X of nearly uniform smoothness of a reflexive Banach space satisfies , 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.     

Isomorphically Expansive Mappings in

We show that for any renorming of , the well known fixed point free mappings by Kakutani, Baillon and others are not nonexpansive.

     

The fixed point property for mappings admitting a center

We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators.