Integral transforms for logharmonic mappings
Arbelaez
H
author
Bravo
V
author
Hernandez
R
author
Sierra
W
author
Venegas
O
author
2021
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 have been developed in search of its proof. It is in this context that the integral transformations of the type f(alpha)(z) = integral(z)(0)(f(zeta)/zeta)(alpha)d zeta or F-alpha(z) = integral(z)(0)(f '(zeta))(alpha)d zeta appear. In this note we extend the classical problem of finding the values of alpha is an element of C for which either f(alpha) or F-alpha are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of logharmonic mappings by considering the extension of the shear construction introduced by Clunie and Sheil-Small in (Clunie and Sheil-Small in Ann. Acad. Sci. Fenn., Ser. A I 9:3-25, 1984) to this new scenario.
Integral transform
Logharmonic mappings
Shear construction
Univalent mappings
WOS:000626943300001
exported from refbase (show.php?record=1354), last updated on Mon, 12 Apr 2021 16:05:31 -0400
text
10.1186/s13660-021-02578-y
Arbelaez_etal2021
Journal of Inequalities and Applications
J. Inequal. Appl.
2021
continuing
periodical
academic journal
2021
1
48
1029-242X