6 papers
A Characterization of concave mappings
V. Bravo, R. Hernández, O. Venegas
This study focuses on Concave mappings, a class of univalent functions that exhibit a unique property: they map the unit disk onto a domain whose complement is convex. The main obj…
Two-point distortion theorems for harmonic mappings
Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas
We establish two-point distortion theorems for sense-preserving planar harmonic mappings which satisfies the univalence criteria in the unit disc such that, Beck…
Integral transform for Logharmonic mappings
H. Arbeláez, V. Bravo, R. Hernández +2
Bieberbach's conjecture was very important in the development of Geometric Function Theory, not only because of the result itself, but also due to the large amount of methods that…
Pre-Schwarzian derivative for Logharmonic mapppings
V. Bravo, R. Hernandez, O. Venegas
We introduce a new definition of pre-Schwarzian derivative for logharmonic mappings and basic properties such as the chain rule, multiplicative invariance and affine invariance are…
A new approach for the univalence of certain integral of harmonic mappings
Hugo Arbeláez, Víctor Bravo, Rodrigo Hernández +2
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 or $f_α(z)=\int_0^z…
Pre-Schwarzian and Schwarzian derivatives of harmonic mappings
Rodrigo Hernández, María J. Martín
In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping in the complex plane without assuming any…