We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that ...

In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level of generality among ...

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects ...

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects ...

We describe and analyze the first adaptive algorithm for merging k convex hulls in the plane. This merging algorithm in turn yields a synergistic algorithm to compute the convex hull of a set of planar points, taking ...

Using techniques of convex analysis, we provide a direct proof of a recent characterization of convexity given in the setting of Banach spaces in [J. Saint Raymond, J. Nonlinear Convex Anal., 14 (2013), pp. 253-262]. Our ...

A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion ...

Many problems of theoretical and practical interest involve finding a convex or concave function.For instance, optimization problems such as finding the projection on the convex functions in $H^k(Omega)$, or some problems ...

The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral ...