Related papers: Certain subclass of harmonic univalent functions d…

We construct a family of bilinear differential operators which satisfy certain gauge properties. These operators can be naturally associated with $q$-deformations of classical integrable hierarchies. In particular, we consider the case when…

We use the Baernstein star-function to investigate several questions about the integral means of the convolution of two analytic functions in the unit disc. The theory of univalent functions plays a basic role in our work.

Let ${\mathcal A}$ be the class of functions analytic in the unit disk ${\mathbb D} := \{ z\in {\mathbb C}:\, |z| < 1 \}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we study the class $\mathcal{U}(\lambda)$,…

Let $\mathcal{S}_u^*$ denote 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 satisfies the inequality $\left|zf'(z)/f(z)-1\right|<1$ in $\mathbb{D}$. In…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

Let $\mathcal{H}_0$ denote the set of all sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\ID$, normalized with $h(0)=g(0)=g'(0)=0$ and $h'(0)=1$. In this paper, we investigate some properties of certain subclasses…

We obtain Schwarz-Pick lemma for $(\alpha, \beta)$-harmonic functions u in the disc, where $\alpha$ and $\beta$ are complex parameters satisfying $\Re \alpha + \Re \beta > -1$. We prove sharp estimate of derivative at the origin for such…

We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…

In certain classes of subharmonic functions u on C distinguished in terms of lower bounds for the Riesz measure of u, a sharp estimate is obtained for the rate of approximation by functions of the form log |f(z)|, where f is an entire…

Let D denote the Dirac operator in the Euclidean space R^m. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic functions by considering the equation DfD=0. The solutions of…

In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic $\Phi$-like functions in the unit disk. The new criterion stated in this…

We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…

We consider a new subclass $\widetilde{\mathcal{K}}_u$ of close-to-convex functions in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$. For this class, we obtain sharp estimates of the Fekete-Szeg\"{o} problem, growth and distortion…

Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent…

In the present paper we introduce and investigate an interesting subclass K_{s}^{(k)}({\gamma},p) of analytic and p-valently close-to-convex functions in the open unit disk U. For functions belonging to this class, we derive several…

We use the notion of radial derivative to introduce composition-differentiation operators on the Hardy and Bergman spaces of the unit ball and the polydisk. We seek for necessary and sufficient conditions on the inducing functions to ensure…

A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…

In this paper we consider some properties of Jackson's difference operator for convex univalent functions in $|z|<1$ with complex parameter $q$ as a Hadamard product of two power series. Jackson in 1908 introduced for a real $q$,…

We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.

Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion…