In this work we give an extension of the Brondsted-Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous epi-pointed functions defined in locally convex spaces. We use a new ...

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 ...

We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of ...

© 2019 Heldermann Verlag. All rights reserved.In this work we prove that if X is a complete locally convex space and {equation presented} is a function such that f -x∗attains its minimum for every x∗∈ U, where U is an open ...

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 ...

Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and ...

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 ...

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 ...