| Records |
| Author |
Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. |
| Title |
Integral transforms for logharmonic mappings |
Type |
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| Year |
2021 |
Publication |
Journal of Inequalities and Applications |
Abbreviated Journal |
J. Inequal. Appl. |
| Volume |
2021 |
Issue |
1 |
Pages |
48 |
| Keywords |
Integral transform; Logharmonic mappings; Shear construction; Univalent mappings |
| Abstract |
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. |
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| ISSN |
1029-242X |
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WOS:000626943300001 |
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UAI @ alexi.delcanto @ |
Serial |
1354 |
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| Author |
Bravo, V.; Hernandez, R.; Ponnusamy, S.; Venegas, O. |
| Title |
Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings |
Type |
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| Year |
2022 |
Publication |
Monatshefte Fur Mathematik |
Abbreviated Journal |
Monatsh. fur Math. |
| Volume |
199 |
Issue |
4 |
Pages |
733-754 |
| Keywords |
Pre-Schwarzian and Schwarzian derivatives; Harmonic and logharmonic mappings; Univalence criterion |
| Abstract |
We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. |
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| ISSN |
0026-9255 |
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WOS:000750771000001 |
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UAI @ alexi.delcanto @ |
Serial |
1531 |
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