Related papers: Starlikeness Associated With The Exponential Funct…

In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new class…

We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1).…

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…

The association of subordination and special functions is used to find sharp estimates on the parameter $\beta$ such that the analytic function $p(z)$ is subordinate to certain functions having positive real part whenever $p(z)+\beta z…

A starlike univalent function $f$ is characterized by the function $zf'(z)/f(z)$; several subclasses of these functions were studied in the past by restricting the function $zf'(z)/f(z)$ to take values in a region $\Omega$ on the right-half…

Let $f$ and $g$ be analytic functions on the open unit disk of the complex plane with $f/g$ belonging to the class $\mathcal{P} $ of functions with positive real part consisting of functions $p$ with $p(0)=1$ and $\operatorname{Re} p(z)>0$…

In this paper, we considered a generalized class of starlike functions defined by Kanas and R\u{a}ducanu\cite{10} to obtain integral means inequalities and subordination results. Further, we obtain the for various subclasses of starlike…

We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class…

In this paper, we investigate two subclasses of analytic and univalent functions associated with the exponential mapping $\varphi(z)=e^{\alpha z},\qquad 0<\alpha\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec…

This paper presents several results concerning second and third-order differential subordination for the class $\mathcal{S}^{*}_{e}:=\{f\in \mathcal{A}:zf'(z)/f(z)\prec e^z\}$, which represents the class of starlike functions associated…

Let A_n be the class of functions f(z) which are analytic in the open unit disk U} with f(0)=0, f'(0)=1, f"(0)=f"'(0)=...=f^{(n)}=0 and f^{(n+1)}\neq0. Applying the results due to S. S. Miller (J. Math. Anal. Appl. 65(1978), 289-305), some…

Let $\mathcal{S}^*(\alpha_1,\alpha_2)$, where $ \alpha_1, \alpha_2 \in (0,1]$, represent the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$, normalized by $f(0) = f'(0) - 1=0$, and satisfying the following…

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…

For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=0, S. S. Miller and P. T. Mocanu (Integral Transform. Spec. Funct. 19(2008)) have considered some sufficient problems for starlikeness. The object of the present paper is…

Let $p$ be an analytic function defined on the open unit disc $\mathbb{D}$ with $p(0)=1$ and $0< \alpha \leq 1$. The conditions on complex valued functions $C$, $D$ and $E$ are obtained for $p$ to be subordinate to $((1+z)/(1-z))^{\alpha}$…

For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $…

Let $h$ be a non-vanishing analytic function in the open unit disc with $h(0)=1$. Consider the class consisting of normalized analytic functions $f$ whose ratios $f(z)/g(z)$, $g(z)/z p(z)$, and $p(z)$ are each subordinate to $h$ for some…

In this paper, we introduce and investigate the subclass $\mathcal{P}_{p,q}^{\xi ,\kappa}(\tau, \eta)$ of starlike functions with negative coefficients by using the differential operator $\Upsilon_{\tau ,p,q}^{\xi ,\kappa}$. Coefficient…

Sharp estimates on $\beta$ are determined so that an analytic function $p$ defined on the open unit disk in the complex plane normalized by $p(0)=1$ is subordinate to some well known starlike functions with positive real part whenever…

Let $\Omega$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=f'(0)-1=0$ and satisfying the inequality \begin{equation*} \left|zf'(z)-f(z)\right|<\frac{1}{2}\quad(z\in\Delta).…