Convexity and constructive infima

Convexity and Osculation in Normed Spaces

Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation, are constructively invalid. The methods used are in accord with principles introduced by Errett Bishop.

Near convexity, metric convexity, and convexity

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Calculating Cost Efficiency with Integer Data in the Absence of Convexity

One of the new topics in DEA is the data with integer values. In DEA classic models, it is assumed that input and output variables have real values. However, in many cases, some inputs or outputs can have integer values. Measuring cost efficiency is another method to evaluate the performance and assess the capabilities of a single decision-making unit for manufacturing current products at a min...

Are Time Consistent Valuations Information Monotone?

Multi-period risk functionals assign a risk value to discrete-time stochastic processes. While convexity and monotonicity extend in straightforward manner from the singleperiod case, the role of information is more problematic in the multi-period situation. In this paper, we define multi-period functionals in such a way that the development of available information over time (expressed as a fil...