In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that...

S-quasiconvex functions (Phu and An, Optimization, Vol. 38, 1996) are stable with respect to the properties: “every lower level set is convex", “each local minimizer is a global minimizer", and “each stationary point is a global minimizer" (i.e., these properties remain true if a sufficiently small linear disturbance is added to a function of this class). In this paper, we introduce a subclass ...

In this theoretical paper we consider the problem of accurately triangulating a scene plane. Rather than first triangulating a set of points and then fitting a plane to these points, we try to minimize the back-projection errors as functions of the plane parameters directly. As this is both geometrically and statistically meaningful our method performs better than the standard two step procedur...

An open question in the study of quasiconvex function is the characterization of the class of functions which are sum of quasiconvex functions. In this paper we restrict attention to quasiconvex radiant functions, i.e. those whose level sets are radiant as well as convex and deal with the claim that a function can be expressed as the sum of quasiconvex radiant functions if and only if it is rad...