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arXiv · 1606.01063

Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness

Amra Rekic-Vukovic·Nermin Okicic·Vedad Pasic·Ivan Arandjelovic
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Abstract

We consider the modulus of noncompact convexity $\Delta_{X,\phi}(\varepsilon)$ associated with the minimalizable measure of noncompactness $\phi$. We present some properties of this modulus, while the main result of this paper is showing that $\Delta_{X,\phi }(\varepsilon)$ is a subhomogenous and continuous function on $[0,\phi (\bar{B}_X))$ for an arbitrary minimalizable measure of compactness $\phi$ in the case of a Banach space $X$ with the Radon-Nikodym property.

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Amra Rekic-Vukovic, Nermin Okicic, Vedad Pasic, Ivan Arandjelovic. 2016-06-03. Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness. https://arxiv.org/abs/1606.01063

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