This paper establishes a necessary and sufficient condition for the convexity (or supermodularity) in oligopoly games.  1999 Elsevier Science B.V. All rights reserved.

Any finite, separately convex, positively homogeneous function on R is convex. This was first established in [1]. In this paper, we give a new and concise proof of this result, and we show that it fails in higher dimension. The key of the new proof is the notion of perspective of a convex function f , namely, the function (x, y) → yf(x/y), y > 0. In recent works [9, 10, 11], the perspective has...

In this work we study the relation between restricted dissimilarity functions-and, more generally, dissimilarity-like functionsand penalty functions and the possibility of building the latter using the former. Several results on convexity and quasiconvexity are also considered.

In this paper, we consider constrained multicriteria continuous location problems in two-dimensional spaces. In the literature, the continuous multicriteria location problem in two-dimensional spaces has received special attention in the last years, although only particular instances of convex functions have been considered. Our approach only requires the functions to be strictly quasiconvex an...

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

We provide a necessary and sufficient condition for strict local minimisers of differences of convex (DC) functions, as well as related results pertaining to characterisation of (non-strict) local minimisers, and uniqueness of global minimisers.

A study of the remainder term in the first order conical development of a convex function is given in the framework of infinite dimensional normed spaces. Lower and upper estimates of this remainder are tackled, and the action of the conjugacy operation on these estimates is characterized. In particular, we shed some light on the duality between the class of conically differentiable convex func...

We deal with only finite point sets P in the plane in general position. A point set is convex or in convex position if it determines a convex polygon. A convex subset Q of P is said to be empty if no point of P lies inside the convex hull of Q. An empty convex subset of P with k elements is also called a k-hole of P . Let P be an n planar point set in general position. For a subset Q of P , den...

Let us introduce the notation used throughout the paper. For any notions related to convexity in this paper, consult R. Schneider [8]. We write o to denote the origin in the Euclidean space En, and ‖ · ‖ to denote the corresponding Euclidean norm. Given a set X ⊂ En, the affine hull and the convex hull of X are denoted by affX and convX , respectively, moreover the interior of X is denoted by i...