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...

In this technical note we give a short proof based on standard results in convex analysis of some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is slightly general since we do not specify the convex set X. For clarity we use the same notation for the different equivalent optimization problems as done in [1]. Free keywords global optimalization, single ...

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TSm α, β, γ . In particular, we obtain integral means ineq...

We focus on the problem of minimizing a convex function f over a convex set S given T queries to a stochastic first order oracle. We argue that the complexity of convex minimization is only determined by the rate of growth of the function around its minimizer xf,S , as quantified by a Tsybakov-like noise condition. Specifically, we prove that if f grows at least as fast as ‖x − xf,S‖ around its...