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Turkish Journal of Mathematics

Journal

2020

Univalent functions

Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik Jan 2020

Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik

Turkish Journal of Mathematics

In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.


General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali Jan 2020

General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali

Turkish Journal of Mathematics

We prove for univalent functions $f(z)=z+\sum_{k=n}^{\infty}a_k z^k;(n\geq 2)$ in the unit disk $\mathbb{U}=\{z:\; z


Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam Jan 2020

Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam

Turkish Journal of Mathematics

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.


On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker Jan 2020

On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker

Turkish Journal of Mathematics

In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.