On the Fekete‐Szegö problem

B A Frasin,Maslina Darus

doi:10.1155/s0161171200005111

B A Frasin, Maslina Darus

Open Access

https://doi.org/10.1155/s0161171200005111

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Abstract

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

Highlights

Let Ꮽ denote the family of functions of the form
Which are analytic in the open unit disk ᐁ = {z : |z| < 1}
A function f (z) belonging to Ꮽ is said to be strongly starlike of order β and type α in ᐁ, and denoted by ᏿ ̄α∗(β) if it satisfies arg zf (z) − α < π β (z ∈ ᐁ)

Summary

Introduction

Let Ꮽ denote the family of functions of the form Let ᏿ denote the class of functions which are univalent in ᐁ. A function f (z) belonging to Ꮽ is said to be strongly starlike of order β and type α in ᐁ, and denoted by ᏿ ̄α∗(β) if it satisfies arg zf (z) − α < π β (z ∈ ᐁ)

Results

Conclusion