Jesús García-Falset

INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS

We study the existence of integral solutions to a class of nonlinear evolution equations of the form where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.

Stability of the Fixed Point Property for Nonexpansive Mappings

In 1971 Zidler [Zi 71] showed that every separable Banach space (X, ‖·‖) admits an equivalent renorming, (X, ‖·‖0), which is uniformly convex in every direction (UCED), and consequently it has weak normal structure and so the weak fixed point property (WFPP) [D-J-S 71].

Fixed point theory for almost convex functions

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Fixed point theory for 1-set contractive and pseudocontractive mappings

The purpose of this paper is to study the existence and uniqueness of fixed point for a class of nonlinear mappings defined on a real Banach space, which, among others, contains the class of separate contractive mappings, as well as to see that an important class of 1-set contractions and of pseudocontractions falls into this type of nonlinear mappings. As a particular case, we give an iterative method to approach the fixed point of a nonexpansive mapping. Later on, we establish some fixed point results of Krasnoselskii type for the sum of two nonlinear mappings where one of them is either a 1-set contraction or a pseudocontraction and the another one is completely continuous, which extend or complete previous results. In the last section, we apply such results to study the existence of solutions to a nonlinear integral equation.

Banach spaces which are r-uniformly noncreasy

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

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.

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

We give a sufficient condition for normal structure more general than the well known ɛ 0 ( X )

Fixed Points for Pseudocontractive Mappings on Unbounded Domains

We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integral equations is given.

Domains of accretive operators in Banach spaces

Let D(A) be the domain of an m -accretive operator A on a Banach space E . We provide sufficient conditions for the closure of D(A) to be convex and for D(A) to coincide with E itself. Several related results and pertinent examples are also included.

Iterative approximation to a coincidence point of two mappings

In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.