# Article ID: MTJPAM-D-20-00042

## Title: Fekete-Szegö Inequalities for Certain Subclasses of Analytic Functions Related with Leaf-Like Domain

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

Article ID: MTJPAM-D-20-00042; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 305-316

Document Type: Research Paper

aSchool of Advanced Science, Vellore Institute of Technology, Deemed to be University, Vellore – 632014, India

Received: 27 November 2020, Accepted: 29 March 2021, Published: 25 April 2021.

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Abstract

The purpose of this paper is to consider coefficient estimates in a class of functions  $\mathscr{M}_{\alpha,\,\lambda}(q)$ consisting of analytic functions  $f$ normalized by   $f(0)=f'(0)-1=0$  in the open unit disk Δ = {z : z ∈ ℂ  and  |z| < 1} subordinating with leaf like domain, to derive certain coefficient estimates a2, a3 and Fekete-Szegö inequality for $f\in\mathscr{M}_{\alpha,\,\lambda}(q)$. A similar results have been done for the function $f^{-1}$. Further application of our results to certain functions defined by convolution products with a normalized functions analytic is given, and in particular we obtain Fekete-Szegö inequalities for certain subclasses of functions defined through Poisson distribution series.

Keywords: Analytic functions, Starlike functions, Convex functions, Subordination, Fekete-Szegö inequality, Poisson distribution series, Hadamard product

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