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Full-Text Articles in Physical Sciences and Mathematics
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Turkish Journal of Mathematics
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Turkish Journal of Mathematics
Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential subordination $\psi(p(z),zp'(z),z^2p''(z);z)\prec h(z)$ implies $p(z)\prec q(z)$, where $p$ is an analytic function in $\mathbb{D}$ with $p(0)=1$, $\psi:\mathbb{C}^3\times \mathbb{D}\to\mathbb{C}$ and $\Omega=h(\mathbb{D})$. This paper investigates the properties of this class for $q(z)=e^z$. As application, several sufficient conditions for normalized analytic functions $f$ to be in the subclass of star-like functions associated with the exponential function are obtained.
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Turkish Journal of Mathematics
In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
Turkish Journal of Mathematics
In a very recent work, Şeker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Salagean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Şeker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions.