Related papers: Manifold approximation of set-valued functions

A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…

It is shown that given a metric space $X$ and a $\sigma$-finite positive regular Borel measure $\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\mu$ measure zero.

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…

In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on…

We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.

This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.

This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.

We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…

An technically interesting proof of a known theorem.

The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…

In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].

We consider the approximation of a continuous function, defined on a compact set of the $d$-dimensional Euclidean space, by sums of two ridge functions. We obtain a necessary and sufficient condition for such a sum to be a best…

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…