Related papers: On relations between the classes $\mathcal S$ and …

It is well-known that the condition ${\operatorname{Re}} \left[1+\frac{zf''(z)}{f'(z)}\right]>0$, $z\in{\mathbb D}$, implies that $f$ is starlike function (i.e. convexity implies starlikeness). If the previous condition is not satisfied for…

Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…

Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc $\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\ID\setminus\{p\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential…

We write the partition function for a lattice gauge theory, with compact gauge group, exactly in terms of unconstrained variables and show that, in the mean field approximation, the dynamics of pure gauge theories, invariant under compact,…

Let be F a family of curves in the unit disc. We show that the set of all functions f holomorphic on the unit disc, which satisfy the following condition, is G-delta and dense in the space of all functions holomorphic on the unit disc: For…

Let $U \subseteq \mathbb C$ be bounded and open. For $0 < \alpha < 1$, $A_\alpha(U)$ is the set of functions in the little Lipschitz class with exponent $\alpha$ that are analytic in a neighborhood of $U$. We consider three conditions,…

In this paper we introduce a class of functions contained in the disc algebra $\mathcal{A}(D)$. We study functions $f \in \mathcal{A}(D)$, which have the property that the continuous periodic function $u = Ref|_{\mathbb{T}}$, where…

For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,}…

Let $N$ be a positive integer. We say a non-constant rational function $U(x)\in{\mathbb C}(x)$ is $N$-\emph{unital} if all the zeros and poles of both $U(x)$ and $1-U(x)$ are either 0 or $N$-th roots of unity. These functions are called…

In this work, we introduce two new subclasses S_{{\Sigma}_{m}}({\alpha},{\lambda}) and S_{{\Sigma}_{m}}(\b{eta},{\lambda}) of {\Sigma}_{m} consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U.…

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…

We consider a family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients,…

Let $Co(\alpha)$ denote the class of concave univalent functions in the unit disk $\ID$. Each function $f\in Co(\alpha)$ maps the unit disk $\ID$ onto the complement of an unbounded convex set. In this paper we find the exact disk of…

In the present investigation, we consider two new subclasses N_{{\Sigma}}^{{\mu}}({\alpha},{\lambda}) and N_{{\Sigma}}^{{\mu}}({\beta},{\lambda}) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper…

We characterize normal families in the unit ball as those families of analytic functions whose restrictions to each complex line through the origin are normal. We then generalize this result to a characterization of normal functions…

For $ -1 \leq B \leq 1$ and $A>B$, let $\mathcal{S}^*[A,B]$ denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions $f$ defined by the subordination $z f'(z)/f(z) \prec (1+ A z)/(1+ B z)$…

In this paper, we define the subclasses $R_{\mu,p}^{\delta}(\alpha;A,B)\ $ and $ P_{\mu,p}^{\delta}(\alpha;A,B)\ $ of analytic functions in the open unit disc of complex plain. Then the neighborhood properties, integral means inequalities…

In this paper, we study the family ${\mathcal C}_{H}^0$ of sense-preserving complex-valued harmonic functions $f$ that are normalized close-to-convex functions on the open unit disk $\mathbb{D}$ with $f_{\bar{z}}(0)=0$. We derive a…

The purpose of the present paper is to find the necessary and sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations…

Let $f_1,f_2$ be linearly independent solutions of $f''+Af=0$, where the coefficient $A$ is an analytic function in the open unit disc $\mathbb{D}$ of $\mathbb{C}$. It is shown that many properties of this differential equation can be…