‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...

We consider the general problem of learning an unknown functional dependency, f : X !→ Y, between a structured input space X and a structured output space Y, from labeled and unlabeled examples. We formulate this problem in terms of data-dependent regularization in Vector-valued Reproducing Kernel Hilbert Spaces (Micchelli & Pontil, 2005) which elegantly extend familiar scalarvalued kernel meth...

The elicitation of a statistic, or property of a distribution, is the task of devising proper scoring rules, equivalently proper losses, which incentivize an agent or algorithm to truthfully estimate the desired property of the underlying probability distribution or data set. Leveraging connections between elicitation and convex analysis, we address the vector-valued property case, which has re...

Quasi-complete, locally convex topological vector spaces V have the useful property that continuous compactly-supported V -valued functions have integrals with respect to finite Borel measures. Rather than constructing integrals as limits following [Bochner 1935], [Birkhoff 1935], et alia, we use the [Gelfand 1936][Pettis 1938] characterization of integrals, which has good functorial properties...