The vector field of a mixed-monotone system is decomposable via decomposition function into increasing (cooperative) and decreasing (competitive) components, this allows for, e.g., efficient computation reachable sets forward invariant sets. A main challenge in approach, however, identifying an appropriate function. In letter, we show that any continuous-time dynamical with Lipschitz continuous...

In recent time, fixed point theory has been developed rapidly in partially ordered metric space. Bhaskar and Lakshmikantham (2006) introduced the concept of mixed monotone property. Lakshmikanthem and Ciric (2009) generalized the concept of mixed monotone mapping and proved a common coupled fixed point theorem. In this paper, we find a new type of contractive condition on Gmetric spaces also th...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory,...

We continue the study of k-monotone Boolean functions in the property testing model, initiated by Canonne et al. (ITCS 2017). A function f : {0, 1} → {0, 1} is said to be kmonotone if it alternates between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in circuit complexity, PAC learni...