The concept of convexity plays an important role in the classical
geometry of normed spaces and it is frequently used in several
branches of nonlinear analysis. In recent years some papers that
contain generalizations of the concept of convexity with the help
of the measures of noncompactness have appeared.
The Tauberian operators were introduced by Kalton and Wilansky
(1976) and they appear in the literature with the aim of
responding to some questions related with the summability and the
factorization of operators; in the preservation by isomorphisms in
Banach spaces, and so forth.
In this paper we make the study of the Tauberian operators, not
starting from the Euclidean distance, but by means of general set
quantities.