Research Article (Funded Research)
On m-Convexity on Real Linear Spaces
Teodoro Lara1*, Nelson Merentes2, Zsolt Pales3, Roy Quintero4, Edgar Rosales1
1Departamento De FiSica Y Matematicas, Universidad De Los Andes, Trujillo, Venezuela.
2Universidad Central de Venezuela. Escuela de matematicas, Caracas, Venezuela.
3Department of Analysis, Institute of Mathematics and Informatics, University of Debrecen, Debrecen, Hungary.
4Department of Mathematics, University of Iowa, USA.
The main purpose of this research is to develop a little further the m-convexity on real linear spaces introduced by Toader in 1984 from the set theoretic point of view. We prove that the family of m-convex sets has the algebraic structure of a complete partial ordered cone and is a proper subfamily of the well known family of star shaped sets respect to the origin. Moreover, we define the corresponding m-convex hull and present a formula to compute it depending on the regular and well known convex hull. Finally, a result of the Caratheodory-type for m-convex sets is shown.
Key word: m-Convexity, m-Convex set, m-Convex hull.