**Title:** Fekete-Szegö Problems for the *k*^{th} 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}

^{a}Department of Mathematics, Institute of Mathematics and Applications, Andharua, Bhubaneswar, Odisha, India

^{b}School of Advanced Sciences, VIT Deemed to be University, Vellore-632014, Tamilnadu, India

^{c}Department 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 corresponding to the root transformation of certain normalized analytic function defined on the unit disk in the complex plane where the function belong to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Further, Fekete-Szegö inequalities for the function and the inverse function for the above mentioned classes are investigated and pointed out the special cases as remark.

**Keywords:** Analytic functions, Subordination, *k*^{th}root transformation, Starlike functions, Convex functions, Fekete-Szegö inequality

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