Related papers: Radius Problems For Functions Associated with a Ne…

Let function $f$ be analytic in the unit disk ${\mathbb D}$ and be normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bounds of the modulus of its second, third and fourth coefficient, if $f$ satisfies \[…

In this paper our aim is to find the radii of starlikeness and convexity for three different kind of normalization of the $N_\nu(z)=az^{2}J_{\nu }^{\prime \prime }(z)+bzJ_{\nu }^{\prime}(z)+cJ_{\nu }(z)$ function, where $J_\nu(z)$ is called…

In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for…

The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1,$ of normalized hyper-Bessel function.

The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find…

Let $\mathcal{A}$ be a unital $\mathbf{C}^*$-algebra with unit $e$. We develop several inequalities for a positive linear functional $f$ on $\mathcal{A}$ and obtain several bounds for the numerical radius $v(a)$ of an element $a\in…

This article examines three radii associated to bounded analytic functions on the polydisk: the well-known Bohr radius, the Bohr-Agler radius, and the Schur-Agler radius. We prove explicit upper and lower bounds for the Bohr-Agler radius,…

For $n\geq 4$ (even), the function $\varphi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk $\mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this paper, the class $\mathcal{S}^*_{n\mathcal{L}} =…

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…

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 $|a_n|\leq cn+d$…

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…

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…

In this article, we consider the family of functions $f$ analytic in the unit disk $|z|<1$ with the normalization $f(0)=0=f'(0)-1$ and satisfying the condition $\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $ for some $0<\lambda \leq…

Let $\mathcal{S}^*(\varphi)$ be the class of all analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfy the subordination relation $zf'(z)/f(z)\prec\varphi(z)$, where…

The radii of convexity of some Lommel and Struve functions of the first kind are determined. For both of Lommel and Struve functions three different normalizations are applied in such a way that the resulting functions are analytic in the…

In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions $f$ in the Ma-Minda type starlike and convex classes $\mathcal{S}^*(\varphi)$ and $\mathcal{C}(\varphi)$, respectively, whenever…

In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions…

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…

We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\frac{1}{z}+b_0+b_1z+b_2z^2+\cdots $$ analytic and locally univalent in the puncture disk $\mathbb{D}_0:=\{z\in\mathbb{C}:\,0<|z|<1\}$. Our first objective in this…

Let ${\mathcal A}$ denote the family of all functions $f$ analytic in the unit disk $\ID$ and satisfying the normalization $f(0)=0= f'(0)-1$. Let $\mathcal{S}$ denote the subclass of ${\mathcal A}$ consisting of univalent functions in…