Related papers: Starlikeness Associated With The Exponential Funct…

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 $F:\mathbb{D}\to\mathbb{C}$…

In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized…

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…

Geometric function theory increasingly draws on $q$-calculus to model discrete and quantum-inspired phenomena. Motivated by this, the present paper introduces new subclasses of analytic functions: the class $\mathcal{S}^{*}_{\xi_q}$ of…

Let A,B,D,E belong to [-1, 1] and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A,B,D,and E are determined so that 1+{\alpha}zp'(z) being subordinated to (1+Dz)/(1+Ez) implies…

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…

Assume that $\Delta$ is the open unit disk in the complex plane and $\mathcal{A}$ is the class of normalized analytic functions in $\Delta$. In this paper we introduce and study the class \begin{equation*} \mathcal{BS}(\alpha):=\left\{f\in…

Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double…

The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic…

We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid…

This paper aims to pursue some classes of normalized analytic functions $f$ with fixed second coefficient defined on open unit disk, such that ${(1+z)^2f(z)}/{z}$ and ${(1+z)f(z)}/{z}$ are functions having positive real part. The radius of…

There are many results for sufficient conditions of functions f(z) which are analytic in the open unit disc U to be starlike and convex in U. The object of the present paper is to derive some interesting sufficient conditions for f(z) to be…

In this paper, we introduce a family of analytic functions given by $$\psi_{A,B}(z):= \dfrac{1}{A-B}\log{\dfrac{1+Az}{1+Bz}},$$ which maps univalently the unit disk onto either elliptical or strip domains, where either $A=-B=\alpha$ or…

Let $\mathcal{H}$ be the class of harmonic functions $f=h+\overline{g}$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, where $h$ and $g$ are analytic in $\mathbb{D}$ with the normalization $h(0)=g(0)=h'(0)-1=0$. Let…

We will provide sufficient conditions for the shifted hypergeometric function $z_2F_1(a,b;c;z)$ to be a member of a specific subclass of starlike functions in terms of the complex parameters $a,b$ and $c.$ For example, we study starlikeness…

Let ${\mathcal M}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition $$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right…

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a…

Let $\mathcal{P}$ denote the Carath\'{e}odory class accommodating all the analytic functions $p$ having positive real part and satisfying $p(0)=1$. In this paper, the second coefficient of the normalized analytic function $f$ defined on the…

Sufficient conditions are obtained on the parameters of Lommel function of the first kind, generalized Struve function of the first kind and the confluent hypergeometric function under which these special functions become exponential convex…

In the present paper, the new generalized classes of (p,q)-starlike and $(p,q)$-convex functions are introduced by using the (p,q)-derivative operator. Also, the (p,q)-Bernardi integral operator for analytic function is defined in an open…