Examples of proper k-ball contractive retractions in F-normed spaces

Abstract

Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r (X) of radius r is properly contained in X. The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a (1 + ε)-ball contractive retraction of B r (X) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X.