This is an announcement for the paper “Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness” by Amra Rekic-Vukovichttp://arxiv.org/find/math/1/au:+Rekic_Vukovic_A/0/1/0/all/0/1, Nermin Okicichttp://arxiv.org/find/math/1/au:+Okicic_N/0/1/0/all/0/1, Vedad Pasichttp://arxiv.org/find/math/1/au:+Pasic_V/0/1/0/all/0/1, Ivan Arandjelovichttp://arxiv.org/find/math/1/au:+Arandjelovic_I/0/1/0/all/0/1.
Abstract: We consider the modulus of noncompact convexity $\Delta_{X, \Phi(\epsilon)}$ 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 $\Delta_{X, \Phi(\epsilon)}$ 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.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.01063