A crossing-free straight-line drawing of a graph is monotone if there is a monotone path between any pair of vertices with respect to some direction. We show how to construct a monotone drawing of a tree with n vertices on an O(n) × O(n) grid whose angles are close to the best possible angular resolution. Our drawings are convex, that is, if every edge to a leaf is substituted by a ray, the (un...

We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain the value ∞. We show that this is true i...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.

Abstract Given a continuous function $$f:{\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : R ? , we denote the so-called “big Lip” and “little lip” functions by "Equation missing" respectively. We are i...

Let $E$ be a uniformly smooth and convex real Banach space $E^*$ its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions use new geometric properties of spaces to show strong convergence an iterative algorithm solution $Ax=0$.

For $C^{1}$-smooth strongly monotone discrete-time dynamical systems, it is shown that “convergence to linearly stable cycles” a prevalent asymptotic behavior in the measure-theoretic sense. The results are then applied several classes of time-periodic parabolic equations and obtain prevalence convergence periodic solutions.