Related papers: Starlikeness Using Special Functions and Subordina…

For $0\leq \alpha <1$, the sharp radii of starlikeness and convexity of order $\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\leq b\leq 1$, and $|a_n|\leq n…

In 2011, Sok\'{o}{\l} (Comput. Math. Appl. 62, 611--619) introduced and studied the class $\mathcal{SK}(\alpha)$ as a certain subclass of starlike functions, consists of all functions $f$ ($f(0)=0=f'(0)-1$) which satisfy in the following…

Let $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ be analytic in the unit disk with second coefficient $a_2$ satisfying $|a_2|=2b$, $0\leq b\leq1$. Sharp radius of Janowski starlikeness and other radius constants are obtained when $|a_n|\leq cn+d$…

The theory of first-order differential subordination developed by Miller and Mocanu was recently extended to functions with fixed initial coefficient by R. M. Ali, S. Nagpal and V. Ravichandran [Second-order differential subordination for…

The radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1$, have been determined for normalizations of $q$-Bessel function, Bessel function of first kind…

We introduce a class of analytic functions subordinate to the function $1+\sinh \left( z\right) $ and obtain various necessary and sufficient conditions for functions to be in the class. These conditions mainly comprise of the coefficient…

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…

Let -1\leq B<A\leq 1. Condition on \beta, is determined so that 1+\beta zp'(z)/p^k(z)\prec(1+Az)/(1+Bz)\;(-1<k\leq3) implies p(z)\prec \sqrt{1+z}. Similarly, condition on \beta is determined so that 1+\beta zp'(z)/p^n(z) or p(z)+\beta…

For functions $f(z)=z^p+a_{n+1}z^{p+1}+...$ defined on the open unit disk, the condition $\Re (f'(z)/z^{p-1})>0$ is sufficient for close-to-convexity of $f$. By making use of this result, several sufficient conditions for close-to-convexity…

Let $\mathcal{A}$ be the family of analytic and normalized functions in the open unit disc $|z|<1$. In this article we consider the following classes \begin{equation*} \mathcal{R}(\alpha,\beta):=\left\{ f\in \mathcal{A}: {\rm…

External occulters, otherwise known as starshades, have been proposed as a solution to one of the highest priority yet technically vexing problems facing astrophysics - the direct imaging and characterization of terrestrial planets around…

For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma…

For a function $f$ starlike of order $\alpha$, $0\leqslant \alpha <1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $\mathbb{D}$ and $\beta>0$, we consider the function $F:\mathbb{D}\to\mathbb{C}$…

Recent advances in image and signal processing have drawn on geometric function theory, particularly coefficient estimate problems. Motivated by their significance, we introduce a class of starlike functions related to a balloon-shaped…

We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…

For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=0, P. T. Mocanu (Mathematica (Cluj), 11(34) (1969)) have considered Mocanu functions. The object of the present paper is to discuss some sufficient problems for f(z) to…

A starlike function $f$ is characterized by the quantity $zf'(z)/f(z)$ lying in the right half-plane. This paper deals with sharp bounds for certain symmetric Toeplitz determinants whose entries are the coefficients of the functions $f$ for…

The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > \alpha|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.

We introduce and study the following special type of differential subordination implication: \begin{equation}\label{abs} p(z)Q(z)+\frac{zp'(z)}{\beta p(z)+\alpha}\prec h(z)\quad\Rightarrow p(z)\prec h(z), \end{equation} which generalizes…

Let $\lambda$ be a real number with $-\pi/2<\lambda<\pi/2.$ In order to study $\lambda$-spirallike functions, it is natural to measure the angle according to $\lambda$-spirals. Thus we are led to the notion of $\lambda$-argument. This fits…