S Ponnusamy
Articles written in Proceedings – Mathematical Sciences
Volume 101 Issue 3 December 1991 pp 219-226
Subordination properties of certain integrals
Let B_{1}(
Volume 103 Issue 1 April 1993 pp 73-89
Convolution properties of some classes of meromorphic univalent functions
Convolution technique and subordination theorem are used to study certain class of meromorphic univalent functions in the punctured unit disc.
Volume 108 Issue 2 June 1998 pp 95-108
On Ramanujan asymptotic expansions and inequalities for hypergeometric functions
In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functions
Volume 118 Issue 3 August 2008 pp 357-370
Decomposition and Removability Properties of John Domains
In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain 𝐷 in $\mathbb{R}^n$ is a John domain if and only if $D\backslash P$ is a John domain, where 𝑃 is a subset of 𝐷 containing finitely many points of 𝐷. The best possibility and an application of the second result are also discussed.
Volume 119 Issue 5 November 2009 pp 593-610
Univalence and Starlikeness of Nonlinear Integral Transform of Certain Class of Analytic Functions
M Obradović S Ponnusamy P Vasundhra
Let $\mathcal{U}(\lambda, \mu)$ denote the class of all normalized analytic functions 𝑓 in the unit disk $|z| < 1$ satisfying the condition
\begin{equation*}\frac{f(z)}{z}\neq 0\quad\text{and}\quad\left|f'(z)\left(\frac{z}{f(z)}\right)^{\mu +1}-1\right| < \lambda,\quad |z| < 1.\end{equation*}
For $f\in\mathcal{U}(\lambda, \mu)$ with $\mu\leq 1$ and $0\neq\mu_1\leq 1$, and for a positive real-valued integrable function 𝜑 defined on [0,1] satisfying the normalized condition $\int^1_0\varphi(t)dt=1$, we consider the transform $G_\varphi f(z)$ defined by
\begin{equation*}G_\varphi f(z)=z\left[\int^1_0\varphi(t)\left(\frac{zt}{f(tz)}\right)^\mu dt\right]^{-1/\mu 1},\quad z\in\Delta.\end{equation*}
In this paper, we find conditions on the range of parameters 𝜆 and 𝜇 so that the transform $G_\varphi f$ is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class $\mathcal{U}(\lambda, \mu)$.
Volume 120 Issue 1 February 2010 pp 83-96
John Disks, the Apollonian Metric, and Min-Max Properties
The main results of this paper are characterizations of John disks–the simply connected proper subdomains of the complex plane that satisfy a twisted double cone connectivity property. One of the characterizations of John disks is an analog of a result due to Gehring and Hag who found such a characterization for quasidisks. In both situations the geometric condition is an estimate for the domain’s hyperbolic metric in terms of its Apollonian metric. The other characterization is in terms of an arc min-max property.
Volume 122 Issue 4 November 2012 pp 583-595
Equivalent Moduli of Continuity, Bloch's Theorem for Pluriharmonic Mappings in $\mathbb{B}^n$
In this paper, we first establish a Schwarz–Pick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau’s and Bloch’s type theorems for pluriharmonic mappings.
Volume 125 Issue 3 August 2015 pp 277-290
On the coefficient conjecture of Clunie and Sheil-Small on univalent harmonic mappings
In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for a class of univalent harmonic functions which includes functions convex in some direction. Next, we prove growth and covering theorems and some related results. Finally, we propose two conjectures, an affirmative answer to one of which would then imply, for example, a solution to the conjecture of Clunie and Sheil-Small.
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