In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and ...

Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 52 (100), No. 3 (2009), pp. 211-226 (16 pages) We survey results on holomorphic functions (of one ...

Abstract: Kernel methods are among the most popular techniques in machine learning. From a regularization theory perspective, they provide a natural choice for the hypotheses space and the ...

If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...

In this chapter, we will describe the curves in $\mathbb{R}^2$ or $\mathbb{R}^{3}$ as the image of a function. $$\vec{r}(t) = \big(r_{1}(t), r_{2}(t),\dots ,r_{n}(t ...

The techniques of 100-level calculus are applied and extended in the study of infinite series, vector-valued functions and functions of two or more variables. Topics include convergence of power ...

Suppose I have a vector-valued function f(x) = y, where x and y are both vectors of some length (same or different length). f could be evaluated over a regular grid of x values, producing a set of y ...

ABSTRACT: In this paper we apply the directional derivative technique to characterize D-multifunction, quasi D-multifunction and use them to obtain ε-optimality for set valued vector optimization ...