Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">U</mi> </semantics> </math> </inline-formula>...

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Bibliographic Details
Main Authors: Hari M. Srivastava, Qazi Zahoor Ahmad, Maslina Darus, Nazar Khan, Bilal Khan, Naveed Zaman, Hasrat Hussain Shah
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Mathematics
Subjects:
analytic functions
close-to-convex functions
subordination
lemniscate of Bernoulli Hankel determinant
Online Access:https://www.mdpi.com/2227-7390/7/9/848
Description
Summary:In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">U</mi> </semantics> </math> </inline-formula> that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered.
ISSN:2227-7390

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