Continuity properties of weakly monotone Orlicz–Sobolev functions

Continuity of Monotone Functions

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...

Weakly Monotone Averaging Functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions and proves that several fam...

Cone Monotone Functions: Differentiability and Continuity

We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.

Cryptographic properties of monotone Boolean functions

by ‘+’.Wedenote the (vector) complement byx = (x 1 + 1, . . . , xn + 1), and the (Boolean function) complement by f (x) = f(x) + 1, for f ∈ Bn. If we de ne the union as (f ∨ g)(x) = f(x) + g(x) + f(x)g(x) then the double complement operation, f(x) Ü→ f (x), has the following properties: f (x) ∨ g(x) = fg(x), f ∨ g(x) = f (x)g(x) (recall that fg(x) = f(x)g(x)). If x = (x 1 , . . . , xn) and y = ...

Definitions and Properties of Monotone Functions