A representation theorem for real convex functions

A Representation Theorem for Bounded Convex Sets

Representation theorem for convex effect algebras

Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation ...

Representation Theorem for Convex Nonparametric Least Squares

We examine a nonparametric least squares regression model where the regression function is endogenously selected from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions is perfectly represented by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrain...

Fenchel’s duality theorem for nearly convex functions

We present an extension of Fenchel’s duality theorem to nearly convexity, giving weaker conditions under which it takes place. Instead of minimizing the difference between a convex and a concave function, we minimize the subtraction of a nearly concave function from a nearly convex one. The assertion in the special case of Fenchel’s duality theorem that consists in minimizing the difference bet...

Representation Theorem for Fuzzy Functions - Graded Form

In this contribution, we will extend results relating to representability of a fuzzy function using a crisp function. And additionally, we show for which functions there exist fuzzy function of a specific form. Our notion of fuzzy function has a graded character. More precisely, any fuzzy relation has a property of being a fuzzy function that is expressed by a truth degree. And it consists of t...