Title: Geometric properties of a family of univalent functions whose derivative lies in a half-plane
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00040; Volume 4 / Issue 1 / Year 2022, Pages 120-127
Document Type: Research Paper
Author(s): Faroze Ahmad Malik a , Chitaranjan Sharma b
aDepartment of Mathematics, Government Holkar (Model, Autonomous) Science College, Indore (M.P.)-452017, India
bDepartment of Mathematics, Government Holkar (Model, Autonomous) Science College, Indore (M.P.)-452017, India
Received: 5 June 2021, Accepted: 15 November 2021, Published: 11 January 2022.
Corresponding Author: Faroze Ahmad Malik (Email address: malikferooze@gmail.com)
Full Text: PDF
Abstract
Let consist of analytic functions
defined in the open unit disk
satisfying
and
. For 0 ≤ β < 1, let
be the family of functions defined as
In this paper, we determine sharp estimates on for
and find out the arc-length of the boundary curve
. Further, we study the inclusion properties of the sequences of partial sums of
.
Keywords: Starlike and convex functions, close-to-convex functions, extremal problems, subordination, arc-length problem
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