The local equicontinuity of a maximal monotone operator

Abstract

The local equicontinuity of an operator $T:X\rightrightarrows X^{\ast }$ with proper Fitzpatrick function ${\phi }_T$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of $\mathrm{Pr}{}_X(\mathrm{dom}{\phi }_T)$). The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space.