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