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, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if m = 0 and f (x) = lnx if m = 0 , the necessary and sufficient conditions for f -convexity (is called Schur m -power convexity) of Daróczy means are given, which improve, generalize and unify Shi et...

We continue the investigation of computational aspects of restricted-orientation convexity (O-convexity) in two dimensions. We introduce one notion of an O-halfplane, for a set O of orientations, and we investigate O-connected convexity. The O-connected convex hull of a nite set X can be computed in time O(jXj log jXj + jOj). The O-connected hull is a basis for determining the O-convex hull of ...

the object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk

The calculation of RTS amounts to measuring a relationship between inputs and outputs in a production structure. There are many methods to measure RTS in the primal space or the dual space. One of the main approaches is using the multiplier on the convexity constraint. But returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constr...