In this paper, we investigate some nonlinear delay integral inequalities and their analogues which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain delay differential equations, delay integral equations and delay difference equations.

BACKGROUND Some effective public health interventions may increase inequalities by disproportionately benefiting less disadvantaged groups ('intervention-generated inequalities' or IGIs). There is a need to understand which types of interventions are likely to produce IGIs, and which can reduce inequalities. METHODS We conducted a rapid overview of systematic reviews to identify evidence on I...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...