Related papers: On the radius constants for classes of analytic fu…
We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.
Recently, Charpentier showed that there exist holomorphic functions $f$ in the unit disk such that, for any proper compact subset $K$ of the unit circle, any continuous function $\phi$ on $K$ and any compact subset $L$ of the unit disk,…
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 paper we investigate an interesting subclass $\mathcal{BS}(\alpha)$ ($0\leq \alpha<1$) of starlike functions in the unit disk $\Delta$. The class $\mathcal{BS}(\alpha)$ was introduced by Kargar et al. [R. Kargar, A. Ebadian and J.…
Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…
We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm,…
In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr…
The function $G_\alpha(z)=1+ z/(1-\alpha z^2)$, \, $0\leq \alpha <1$, maps the open unit disc $\mathbb{D}$ onto the interior of a domain known as the Booth lemniscate. Associated with this function $G_\alpha$ is the recently introduced…
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…
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit…
In this paper our aim is to find the radii of $\gamma$-Spirallike of order $\alpha$ and convex $\gamma$-Spirallike of order $\alpha$ for three different kinds of normalizations of the function…
Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark measures and in terms of their…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error…
In this paper we introduced the class $\mathcal{S}_{G}^{\ast }$ of analytic functions which is related with starlike functions and generating function of Gregory coefficients. By using bounds on some coefficient functionals for the family…
Let u be a subharmonic function in D={|z|<1}. There exist an absolute constant C and an analytic function f in D such that \int_D |u(z)-log|f(z)|| dm(z)<C where m denotes the plane Lebesgue measure. We also consider uniform approximation.
A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described.
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…
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…