Abstract
AbstractThis paper considers a special class $$S_{L}(h)$$
S
L
(
h
)
of logharmonic mappings of the form $$f(z)=h(z)\overline{h^{\prime }(z)},$$
f
(
z
)
=
h
(
z
)
h
′
(
z
)
¯
,
where h is analytic in the unit disk U, normalized by $$h(0)=0$$
h
(
0
)
=
0
, $$h^{\prime }(0)=1$$
h
′
(
0
)
=
1
, and h(U) is starlike. For this class of functions, a distortion theorem is proved, and Bohr’s inequality along with some improvements and refinements is investigated. In addition, the radius of starlikeness and an estimate for arclength are obtained.
Funder
Carnegie Mellon University Qatar
Publisher
Springer Science and Business Media LLC
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