In this paper, we reveal a relation between joint winner property (JWP) in the field of valued constraint satisfaction problems (VCSPs) and M-convexity in the field of discrete convex analysis (DCA). We introduce the M-convex completion problem, and show that a function f satisfying the JWP is Z-free if and only if a certain function f associated with f is M-convex completable. This means that ...

In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.

This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.

In the first part of this investigation, [1], we generalized a weighted distance function of [2] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so–called M–relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generaliza...

In this paper, we introduce a new convexity on graphs similar to the well known P3convexity [3], which we will call P ∗ 3 -convexity. We show that several P ∗ 3 -convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We show a strong relation between this convexity and the well known geo...

In this paper we give some useful combinatorial properties of polynomial paths. We also introduce generalized majorization between three sequences of integers and explore its combinatorics. In addition, we give a new, simple, purely polynomial proof of the convexity lemma of E. M. de Sá and R. C. Thompson. All these results have applications in matrix completion theory.

In their study of a quartic integral, Boros and Moll discovered a special class of sequences, which is called the Boros–Moll sequences. In this paper, we consider the concavity and convexity of the Boros–Moll sequences {di(m)}i=0. We show that for any integer m > 6, there exist two positive integers t0(m) and t1(m) such that di(m)+di+2(m) > 2di+1(m) for i ∈ [0, t0(m)] ⋃ [t1(m),m−2] and di(m)+di...