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On $λ$ -pseudo starlike functions associated with vertical strip domain

Janusz Sokół

University of Rzeszów, College of Natural Sciences, ul. Prof. Pigonia 1, 35-310, Rzeszów, Poland

E-mail Address: jsokol@ur.edu.pl

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G. Murugusundaramoorthy

School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamilnadu, India

E-mail Address: gmsmoorthy@yahoo.com

Corresponding author.

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, and

K. Vijaya

School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamilnadu, India

E-mail Address: kvijaya@vit.ac.in

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https://doi.org/10.1142/S1793557123501358Cited by:3 (Source: Crossref)

Abstract

We consider the class of $λ$ -pseudo starlike functions $f (z) = z + a_{2} z^{2} + a_{3} z^{3} + \dots$ such that $z {(f^{'} (z))}^{λ} / f (z)$ maps the open unit disk $| z | < 1$ onto a strip domain $w$ with $\frac{α - π}{2 sin α} < ℜ (w (z)) < \frac{α}{2 sin α}$ for some $α$ , $π / 2 \leq α < π$ . We estimate $| a_{2} |$ , $| a_{3} |$ and solve the Fekete–Szegö problem for functions in this class.

Communicated by A. Escassut

Keywords:

AMSC: 30C45, 30C50

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