Logarithmic Coefficients for Univalent Functions Defined by Subordination

Ebrahim Analouei Adegani,Nak Eun Cho,Mostafa Jafari

doi:10.3390/math7050408

Ebrahim Analouei Adegani, Nak Eun Cho + Show 1 more

Open Access

https://doi.org/10.3390/math7050408

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Abstract

In this work, the bounds for the logarithmic coefficients γ n of the general classes S * ( φ ) and K ( φ ) were estimated. It is worthwhile mentioning that the given bounds would generalize some of the previous papers. Some consequences of the main results are also presented, noting that our method is more general than those used by others.

Highlights

Let H denote the class of analytic functions in the open unit disk U := {z ∈ C : |z| < 1} and A
Based on the results presented in previous research, in the current study, the bounds for the logarithmic coefficients γn of the general classes S ∗ ( φ) and K( φ) were estimated
Throughout this paper, we assume that φ is an analytic univalent function in the unit disk U

Summary

Introduction

Let H denote the class of analytic functions in the open unit disk U := {z ∈ C : |z| < 1} and A denote the subclass of H consisting of functions of the form. Ma and Minda [2], in which either of the quantity f (z) or 1 + f 0 (z) is subordinate to a more general superordinate function To this aim, they considered an analytic univalent function φ with positive real part in U. Φ(U) is symmetric respecting the real axis and starlike considering φ(0) = 1 and φ0 (0) > 0 They defined the classes consisting of several well-known classes as follows:. S ∗ := S ∗ (0) and K := K(0) are the class of starlike functions and of convex functions in the unit disk U, respectively. Based on the results presented in previous research, in the current study, the bounds for the logarithmic coefficients γn of the general classes S ∗ ( φ) and K( φ) were estimated.

Main Results

Letting

Taking cz

Results