Article ID: MTJPAM-D-20-00054

Title: Fekete-Szegö Problems for the kth Root Transform of Subclasses of Starlike and Convex Functions with Respect to Symmetric Points


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00054; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 172-181

Document Type: Research Paper

Author(s): Trailokya Panigrahi a , Gangadharan Murugusundaramoorthy b , Susanta Kumar Mohapatra c

aDepartment of Mathematics, Institute of Mathematics and Applications, Andharua, Bhubaneswar, Odisha, India

bSchool of Advanced Sciences, VIT Deemed to be University, Vellore-632014, Tamilnadu, India

cDepartment of Mathematics, Kalinga Institute of Social Sciences (KISS) Deemed to be University, Bhubaneswar-751024, Odisha, India

Received: 26 December 2020, Accepted: 1 February 2021, Published: 25 April 2021.

Corresponding Author: Trailokya Panigrahi (Email address: trailokyap6@gmail.com)

Full Text: PDF

Abstract

In the present paper, sharp upper bounds for the coefficient functional |b_{2k+1}-\mu b_{k+1}^{2}| corresponding to the k^{th} root transformation of certain normalized analytic function f(z)=z+\sum_{n=2}^{\infty}a_{n}z^{n} defined on the unit disk  \Delta  in the complex plane where the function  f(z)  belong to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Further, Fekete-Szegö inequalities for the function  \frac{z}{f(z)}  and the inverse function f for the above mentioned classes are investigated and pointed out the special cases as remark.

Keywords: Analytic functions, Subordination, kthroot transformation, Starlike functions, Convex functions, Fekete-Szegö inequality

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