Univalent functions, fractional calculus, and their applications , edited by H. M. Srivastava and S. Owa. Pp 404. £39·95. 1989. ISBN 0-7458-0701-1 (Ellis Horwood)

On differential subordinations (単葉関数論の歴史的定理の新展開について)

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

On the theory of multivalent functions

In the present investigation, our aim is to define a generalized subclass of analytic and bi-univalent functions associated with a certain $q$-integral operator in the open unit disk $\mathbb{U}$. We estimate bounds on the initial Taylor-Maclaurin coefficients $\left \vert a_{2}\right \vert$ and $\left \vert a_{3}\right \vert $ for normalized analytic functions $f$ in the open unit disk by considering the function $f$ and its inverse $g = f^{{-}{1}}$. Furthermore, we derive special consequences of the results presented here, which would apply to several (known or new) subclasses of analytic and bi-univalent functions.

Applications of a certain $q$-integral operator to the subclasses of analytic and bi-univalent functions

The aim of the present paper is to study some coefficient problems for certain classes associated with starlike functions such as sharp bounds for initial coefficients, logarithmic coefficients, Hankel determinants and Fekete–Szego problems. Moreover, we obtain some geometric properties as applications of differential subordinations.

Coefficient bounds and differential subordinations for analytic functions associated with starlike functions

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.

https://www.mdpi.com/2227-7390/7/5/408/pdf

Logarithmic Coefficients for Univalent Functions Defined by Subordination

Abstract In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes HqΣ(λ,h),STqΣ(α,h) andMqΣ(α,h) $\\begin{array}{} H_{q}^{\\Sigma}(\\lambda,h),\\, ST_{q}^{\\Sigma}(\\alpha,h)\\,\\text{ and} \\,\\,M_{q}^{\\Sigma}(\\alpha,h) \\end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Republic of Korea

/pdf/logarithmic-coefficient-bounds-and-coefficient-conjectures-b8ckypaaty.pdf

Ebrahim Analouei Adegani

Papers

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Coefficient bounds and differential subordinations for analytic functions associated with starlike functions

Logarithmic Coefficients for Univalent Functions Defined by Subordination

Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions