On harmonic entire mappings
In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping f = h + g ¯ , respectively, and also consider the relationship between the order and the type of f , h , and g . Secondly, we investiga...
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Published in | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping
f
=
h
+
g
¯
, respectively, and also consider the relationship between the order and the type of
f
,
h
, and
g
. Secondly, we investigate the harmonic mappings
f
=
h
+
g
¯
such that
f
(
n
p
)
=
h
(
n
p
)
+
g
(
n
p
)
¯
are univalent in the unit disk, where
{
n
p
}
p
=
1
∞
be a strictly increasing sequence of nonnegative integers. In terms of the sequence
{
n
p
}
p
=
1
∞
, we derive several necessary conditions for these mappings to be entire and also establish an upper bound for the order of these mappings. |
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ISSN: | 1578-7303 1579-1505 |
DOI: | 10.1007/s13398-021-01148-7 |