In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also con...

A new system of nonlinear variational inclusions involving A, η -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with A, η -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since A, η -monotonicity generalizes A-monotonicity and Hmonotonicity, our res...

We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case...

Recently, some new types of monotonicity—in particular, weak monotonicity and directional an n-ary real function—were introduced successfully applied. Inspired by these generalizations monotonicity, we introduce a notion for functions acting on [0,1]n, namely, the shift stability. This property extends standard invariantness (difference scale invariantness), which can be seen as particular The ...

Abstract Is it always beneficial to create a new relationship (have follower/friend) in social network? This question can be formally stated as property of the centrality measure that defines importance actors network. Score monotonicity means adding an arc increases score target arc; rank improves relatively remaining nodes. It is known most centralities are both and monotone on directed, stro...