On the Fekete-SzegÖ Problem for Starlike Functions of Complex Order

Hanan Darwish; Abdel-Moniem Lashin; Bashar Al Saeedi*

doi:10.5666/KMJ.2020.60.3.477

Article

Kyungpook Mathematical Journal 2020; 60(3): 477-484

Published online September 30, 2020

On the Fekete-SzegÖ Problem for Starlike Functions of Complex Order

Hanan Darwish and Abdel-Moniem Lashin, Bashar Al Saeedi*

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516 Egypt
e-mail : darwish333@yahoo.com and aylashin@mans.edu.eg
Department of Mathematics, Faculty of Science & Engineering, Manchester Metropolitan University, Manchester, M15GD, UK
e-mail : basharfalh@yahoo.com

Received: January 28, 2016; Revised: May 3, 2020; Accepted: May 4, 2020

Abstract

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Abstract

For a non-zero complex number b and for m and n in let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ℜ [1+1b(Dn+mf(z)Dnf(z)-1)]>0 in the unit disk U, where Dⁿf(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional ∣a3-μa22∣ are obtained.

Keywords: coefficient estimates, Salagean operator, Fekete Szego problem, starlike functions of complex order