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...

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,...

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.

Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som [11] and Jungck and Sessa [7] and some known results [4], [9], [12] are obtained as consequence. To achieve our goal, we hav...