arXiv subjects

Víctor Bravo

Publications and source records attributed to Víctor Bravo.

4 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↗

arXiv2021

Influence of a function's coefficients and feedback of the mathematical work when reading a graph in an online assessment system

This paper shows the results of an experiment applied to 170 students from two Chilean universities who solve a task about reading a graph of an affine function in an online assessment environment where the parameters (coefficients of the graphed affine function) are randomly defined from an ad-hoc algorithm, with automatic correction and automatic feedback. We distinguish two versions: one of them with integer coefficients and the other one with decimal coefficients in the affine function. We observed that the nature of the coefficients impacts the mathematical work used by the students, where we again focus on two of them: by direct estimation from the graph or by calculating the equation of the line. On the other hand, a feedback oriented towards the "estimation" strategy influences the mathematical work used by the students, even though a non-negligible group persists in the "calculating" strategy, which is partly explained by the perception of each of the strategies.

math.HO↗

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↗