This book presents two natural generalizations of continuous mappings, namely usco and
quasicontinuous mappings. The first class considers set-valued mappings, the second class …

Banach spaces provide a framework for modern mathematical analysis, as they blend
classical analysis, geometry, topology and linearity. This makes Banach space theory a …

A reconstruction technique, mathematically based on a generalization of the gradient
method in Banach spaces, is first proposed to enhance the spatial resolution of radiometer …

In this paper we give new sufficient and necessary conditions for a Banach space to be
equivalently renormed with the Mazur intersection property. As a consequence, several …

Some local versions of the Bishop–Phelps–Bollobás property for operators have been
recently presented in Dantas et al.(J Math Anal Appl 468 (1): 304–323, 2018). In the present …

In this paper, we fully characterize the duality mapping over the space of matrices that are
equipped with Schatten norms. Our approach is based on the analysis of the saturation of …

The strong subdifferentiability of norms (ie\. one-sided differentiability uniform in directions)
is studied in connection with some structural properties of Banach spaces. It is shown that …

We survey various boundedness, differentiability and extendibility properties of convex
functions, and how they are related to sequential convergence with respect to various …

We show that when the duality map is norm-to-weak upper semi-continuous at some point of
a dual space, the pre-duality map shares this property. We show that if x is a point of very …

We study the (uniform) strong subdifferentiability of norms of Banach spaces P (NX, Y*) of all
continuous N-homogeneous polynomials and tensor products of Banach spaces, namely …