# 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)

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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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