Examples of proper k-ball contractive retractions in F-normed spaces |
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| Authors: | D. Caponetti A. Trombetta |
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| Affiliation: | a Department of Mathematics, University of Palermo, I-90123 Palermo, Italy
b Department of Mathematics, University of Calabria, I-87036 Rende (CS), Italy |
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| Abstract: | Assume X is an infinite dimensional F-normed space and let r be a positive number such that the closed ball Br(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 Br(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. |
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| Keywords: | Regular F-normed ideal space Retraction ρ-Near retraction Hausdorff measure of noncompactness k-Ball contraction |
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