On a class of analytic functions governed by subordination
2019 ◽
Vol 11
(1)
◽
pp. 144-155
◽
Keyword(s):
Abstract The purpose of this paper is to introduce a class of functions ℱλ, λ ∈ [0, 1], consisting of analytic functions f normalized by f(0) = f´(0) − 1 = 0 in the open unit disk U which satisfies the subordination condition that $${\rm{z}}f'\left( {\rm{z}} \right)/\left\{ {\left( {1 - \lambda } \right){\rm{f}}\left( {\rm{z}} \right) + \lambda {\rm{z}}} \right\} \prec {\rm{q}}\left( {\rm{z}} \right),\,\,\,\,\,{\rm{z}} \in {\rm{\mathbb{U},}}$$ where ${\rm{q}}\left( {\rm{z}} \right) = \sqrt {1 + {{\rm{z}}^{\rm{2}}}} + {\rm{z}}$ . Some basic properties (including the radius of convexity) are obtained for this class of functions.
Keyword(s):
Keyword(s):
2013 ◽
Vol 21
(1)
◽
pp. 277-284
Keyword(s):
Keyword(s):
2018 ◽
Vol 37
(4)
◽
pp. 173-186
Keyword(s):
2001 ◽
Vol 25
(12)
◽
pp. 771-775
◽
Keyword(s):