Non Parametric Learnability of Income-Lipschitz Demand Functions

POINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

Metric Learning via Maximizing the Lipschitz Margin Ratio

In this paper, we propose the Lipschitz margin ratio and a new metric learning framework for classification through maximizing the ratio. This framework enables the integration of both the inter-class margin and the intra-class dispersion, as well as the enhancement of the generalization ability of a classifier. To introduce the Lipschitz margin ratio and its associated learning bound, we elabo...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.