In this paper, we study the convexity of the integral operator

The aim of the present study was to obtain quantitative information concerning the three-dimensional (3D) arrangement of the facial soft tissues of subjects with Down's syndrome. The 3D co-ordinates of 50 soft tissue facial landmarks were recorded by an electromechanical digitizer in 17 male and 11 female subjects with Down's syndrome aged 12-45 years, and in 429 healthy individuals of the same...

Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of nontraditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity,...

Abstract Convexity is a deeply studied concept since it very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity required as well and some important applications can be found fuzzy optimization, particular sets. In this paper have extended notion for interval-valued sets order to able cover wider area imprecision. We show its interesting propert...

Abstract In this paper, we prove some convexity results associated to orbit projection of noncompact real reductive Lie groups.

Classical convexity can be naturally translated to graphs considering shortest paths, giving rise to the geodesic convexity. Moreover, if we consider induced paths between vertices, we get the so-called monophonic convexity. In this work, we present some results involving monophonic sets.