arXiv subjects

Osvaldo Venegas

Publications and source records attributed to Osvaldo Venegas.

3 recordsLinked to original sources

arXiv2026

A Characterization of $α$-Convex Functions with Sharp Coefficient and Schwarzian Estimates

The class $M_α$ of $α$-convex functions, introduced by Mocanu in 1969, interpolates between starlike and convex functions. We prove a characterization of $M_α$ that extends a theorem of Chuaqui, Duren, and Osgood from the convex case to the full class, and determine sharp values of $β$ for which $M_α\subset C_β$ and $C_β\subset M_α$. We also obtain a sharp Fekete--Szegő inequality, bounds for the order and the Schwarzian norm, and an explicit formula for the Schwarzian norm of the $α$-Koebe function for $α= 1/n$, $n \in \mathbb{N}$, which we verify for $n \leq 9$ and conjecture to hold in general.

math.CV↗

arXiv2022

Two-point distortion theorems for harmonic mappings

We establish two-point distortion theorems for sense-preserving planar harmonic mappings $f=h+\overline{g}$ which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the sharp two-point distortion theorem when $h$ is a convex function, and normalized mappings such that $h(\D)$ is a $c$-linearly connected domain. To do this, we use the order of this family.

math.CV↗

arXiv2019

A new approach for the univalence of certain integral of harmonic mappings

The principal goal of this paper is to extend the classical problem of find the values of $α\in \C$ for which the mappings, either $F_α(z)=\int_0^z(f(ζ)/ζ)^αdζ$ or $f_α(z)=\int_0^z(f'(ζ))^αdζ$ are univalent, whenever $f$ belongs to some subclasses of univalent mappings in $\D$, but in the case of harmonic mappings, considering the \textit{shear construction} introduced by Clunie and Sheil-Small in \cite{CSS}.

math.CV↗