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Papers by Enrique Llorens-Fuster

Fixed Point Theory, 2022

We give here a dichotomic fixed point result for a certain class of mappings defined in the close... more We give here a dichotomic fixed point result for a certain class of mappings defined in the closed unit ball of a Hilbert space. This dichotomy states that, for any of the mappings in this class, either it has a fixed point or its Lipschitz constant with respect to any renorming of 2 has to be strictly greater than 1.

Carpathian Journal of Mathematics, 2015

In this paper we present a fixed point theorem for contractive type multivalued operators in cone... more In this paper we present a fixed point theorem for contractive type multivalued operators in cone metric spaces by using the concept of c-distance.

Journal of Mathematical Analysis and Applications, 1993

Carpathian Journal of Mathematics

In 2011 Aoyama and Kohsaka introduced the α-nonexpansive mappings. Here we present a further stud... more In 2011 Aoyama and Kohsaka introduced the α-nonexpansive mappings. Here we present a further study about them and their relationships with other classes of generalized nonexpansive mappings.

The American Mathematical Monthly, 2020

It is known that some particular self-mappings of the closed unit ball of ℓ2 with no fixed points... more It is known that some particular self-mappings of the closed unit ball of ℓ2 with no fixed points cannot be nonexpansive with respect to any renorming of ℓ2. We give here a short proof of this fact for any closed convex subset of that these mappings leave invariant.

Journal of Fixed Point Theory and Applications, 2018

We present a further study on fixed point theory for the so called iterated nonexpansive mappings... more We present a further study on fixed point theory for the so called iterated nonexpansive mappings, that is, mappings which are nonexpansive along the orbits. They are a direct generalization of a contractions studied by Rheinboldt in the late sixties of the last century. This is a wide class of nonlinear mappings including several families of generalized nonexpansive mappings appearing in the recent litherature.

Nonlinear Analysis: Theory, Methods & Applications, 2003

We consider a family of spaces wider than UNC spaces introduced by Prus, and we give some ÿxed po... more We consider a family of spaces wider than UNC spaces introduced by Prus, and we give some ÿxed point results in the setting of these spaces.

Advances in the Theory of Nonlinear Analysis and its Application

It is defined a class of generalized nonexpansive mappings, which properly contains those defined... more It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.

A very general class of multivalued generalized nonexpansive mappings is defined. We also give so... more A very general class of multivalued generalized nonexpansive mappings is defined. We also give some fixed point results for these mappings, and finally we compare and separate this class from the other multivalued generalized nonexpansive mappings introduced in the recent literature.

We give an example of a renorming of 2 with the fixed-point property (FPP) for nonexpansive mappi... more We give an example of a renorming of 2 with the fixed-point property (FPP) for nonexpansive mappings, but which seems to fall out of the scope of all the com-monly known sufficient conditions for FPP.

Introduction We say a closed convex subset of the Banach space (X; k \Delta k) has the fixed poin... more Introduction We say a closed convex subset of the Banach space (X; k \Delta k) has the fixed point property (fpp) if every nonexpansive mapping T : C \Gamma! C has a fixed point. Here, T nonexpansive means kTx \Gamma Tyk kx \Gamma yk, for all x; y 2 C. We ask which nonempty closed bounded convex subsets of c 0 enjoy the fpp? It is now well known that all nonempty weak compact convex subsets of c 0 have the fpp [Maurey, 1980]. On the other hand, closed bounded convex subsets with a nonempty interior always fail to have the fpp, proposition 1 below. That sets without interior may also fail to have the fpp is demonstrated by B + c 0 := f(xn ) : 0<F42

We find lower bounds for the set of Lipschitz constants of a given Lipschitzian map, defined on t... more We find lower bounds for the set of Lipschitz constants of a given Lipschitzian map, defined on the closed unit ball of a Hilbert space, with respect to any renorming. We introduce a class of maps, defined in the closed unit ball of l 2 , which contains the classical fixed point free maps due to Goebel–Kirk–Thelle, Baillon, and P.K. Lin. We show that for any map of this class its uniform Lipschitz constant with respect to any renorming of l 2 is never strictly less than π 2 .

Fixed Point Theory

In 1987 P.K. Lin found a fixed-point free selfmapping f of a closed convex subset of the unit bal... more In 1987 P.K. Lin found a fixed-point free selfmapping f of a closed convex subset of the unit ball of 2. Here we point out some remarkable features of this mapping. In particular we will show that if | • | is any equivalent renorming of 2 , then f is not nonexpansive with respect to | • | .

Handbook of Metric Fixed Point Theory, 2001

Indeed, there are a lot of quantitative descriptions of geometrical properties of Banach spaces. ... more Indeed, there are a lot of quantitative descriptions of geometrical properties of Banach spaces. The most common way for creating these descriptions, is to define a real function (a “modulus” depending on the Banach space under consideration, and from this define a suitable constant or coefficient closely related to this function. The moduli and/or the constants are attempts to get a better understanding about two things: The shape of the unit ball of a space, and The hidden relations between weak and strong convergence of sequences.

ABSTRACT The space ℓ 1 can be equivalently renormed to enjoy the fixed point property for a large... more ABSTRACT The space ℓ 1 can be equivalently renormed to enjoy the fixed point property for a large class of generalized nonexpansive mappings.