Genaro López Acedo

Firmly nonexpansive mappings in classes of geodesic spaces

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W -hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations. MSC: Primary: 47H09, 47H10, 53C22; Secondary: 03F10, 47H05, 90C25, 52A41.

CONSTRUCTION OF SUNNY NONEXPANSIVE RETRACTIONS IN BANACH SPACES

CONSTRUCTION OF SUNNY NONEXPANSIVE RETRACTIONSIN BANACH SPACESTOMAS DOMINGUEZ BENAVIDES, GENARO LOPEZ ACEDO AN XuD HONG-KUNLet J be commutativ a e famil of nonexpansivy e self-mapping of a closes d convexsubset C of a uniformly smooth Banach X spac suceh that th seet of common fixedpoints is nonempty I. t is shown that if a certain regularity condition is satisfied, thenthe sunny nonexpansive retractio C tno from F can be constructed in an iterativeway.

Random fixed points of set-valued operators

Some random fixed point theorems for set-valued operators are obtained. The measurability of certain marginal maps is also studied. The underlying measurable space is not assumed to be a Suslin family.

Browder's Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces

We give a sufficient and necessary condition concerning a Browders convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces.

On the Topological Degree for A-Compact Mappings

In [ 1 ] F. E. Browder and W. V. Petryshyn develop a generalized degree theory for A-proper mappings. This class of mappings is wider than com- pact perturbations of the identity, for which the classical Leray-Schauder degree is defined. Recently Werinski [S] defined a fixed point index for another class of mappings, called Admissible, which includes compact map- pings but does not include the class of A-proper mappings. In this paper we will define a topological degree for a new class of mappings, which we denote A-compact mappings. We will prove that this class contains the classes of A-proper mappings and Admissible mappings. As an application we shall show some classical topological results for not necessarily A-proper mappings.