Iterated nonexpansive mappings

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 the contraction type maps 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.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Fixed point theory for a class of generalized nonexpansive mappings

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

An overview on the Prus-Szczepanik condition

In 2005 Prus and Sczcepanik introduced a large class of Banach spaces with the fixed point property for nonexpansive mappings. We say that this class satisfies the PSz condition. Checking that a given Banach space belongs to this class is not an easy task. Here we study the relationship between the PSz condition and other well-known geometrical properties of Banach spaces, and we give easier sufficient conditions for a Banach space to satisfy it.Consejo Nacional de Ciencia y Tecnologia (México)Ministerio de Economía y Competitivida

On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces

In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given