| Records |
| Author |
Arbelaez, H.; Hernandez, R.; Sierra, W. |
| Title |
Lower and upper order of harmonic mappings |
Type |
|
| Year |
2022 |
Publication |
Journal Of Mathematical Analysis And Applications |
Abbreviated Journal |
J. Math. Anal. Appl. |
| Volume |
507 |
Issue |
2 |
Pages |
125837 |
| Keywords |
Harmonic mapping; Lower order; Upper order; Concave functions; Linearly connected domain; Schwarzian derivative |
| Abstract |
In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved. |
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Place of Publication |
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| Language |
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Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0022-247X |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000775539700031 |
Approved |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1557 |
| Permanent link to this record |
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| Author |
Chuaqui, M.; Hernandez, R. |
| Title |
Univalent harmonic mappings and linearly connected domains |
Type |
|
| Year |
2007 |
Publication |
Journal Of Mathematical Analysis And Applications |
Abbreviated Journal |
J. Math. Anal. Appl. |
| Volume |
332 |
Issue |
2 |
Pages |
1189-1194 |
| Keywords |
harmonic mapping; univalent; linearly connected domain; second complex dilatation |
| Abstract |
We investigate the relationship between the univalence of f and of h in the decomposition f = h + (g) over bar of a serise-preserving harmonic mapping defined in the unit disk D subset of C. Among other results, we determine the holomorphic univalent maps It for which there exists c > 0 such that every harmonic mapping of the form f = h + (g) over bar with vertical bar g'vertical bar < c vertical bar h'vertical bar is univalent. The notion of a linearly connected domain appears in our study in a relevant way. (c) 2006 Elsevier Inc. All rights reserved. |
| Address |
Catholic Univ Chile, Santiago, Chile, Email: m.chuaqui@mat.puc.cl |
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Thesis |
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| Publisher |
Academic Press Inc Elsevier Science |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0022-247x |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000247120600031 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
42 |
| Permanent link to this record |
