Related papers: A criterion for normality of analytic mappings

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

We prove a Zalcman-Pang lemma in several complex variables and apply it to obtain several complex variables analogues of the known normality criteria like Lappan's five-point theorem and Schwick's theorem.

This paper treats the class of normalized logharmonic mappings f(z) = zh(z)bar{g(z)} in the unit disk satisfying {\phi}(z) = zh(z)g(z) is analytically typically real. Every such mapping f is shown to be a product of two particular…

In this paper, our main aim is to extend a classical theorem of Phelps on norm-attaining functionals from the space of scalar-valued continuous functions $C(\Omega)$ to its vector-valued counterpart $C(\Omega, X)$. One of our main results…

We prove that Allard's regularity theorem holds for rectifiable $n$-dimensional varifolds $V$ assuming a weaker condition on the first variation. This, in the special case when $V$ is a smooth manifold translates to the following: If…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

We determine completely the analytic functions $\varphi$ in the unit disk $\mathbb D$ such that for all (normalized) orientation-preserving harmonic mappings $f=h+\overline g$ produced by the shear construction with $h+g=\varphi$, the…

In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic…

In this paper we prove some analogue of Wiman's type inequality for random analytic functions in the polydisc $\mathbb{D}^p=\{z\in\mathbb{C}^p\colon |z_j|<1, j\in\{1,\ldots,p\}\},\ p\in\mathbb{Z}_+$. The obtained inequality is sharp.

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps…

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

In this paper, we show that harmonic Bloch mappings are Lipschitz continuous with respect to the pseudo-hyperbolic metric. This result improves the corresponding result of Theorem 1 of [P. Ghatage, J. Yan, and D. Zheng, Composition…

We introduce a generalized version of the local Lipschitz number $\textrm{lip}\,u$, and show that it can be used to characterize Sobolev functions $u\in W_{\textrm{loc}}^{1,p}(\mathbb R^n)$, $1\le p\le \infty$, as well as functions of…

Let $\mathbb{B}$ be the unit ball of a complex Banach space $X$. In this paper, we will generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball $\mathbb{B}$ by using the radial derivative. Next, we define an…

In the context of differential fields of characteristic zero with several commuting derivations, we discuss the notion of $\#$-differential equations on parameterized D-torsors and their associated Galois extensions. Using model-theoretic…

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…