A. Swaminathan

activity

20172025

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math.CV2025

Integral representation and functional inequalities involving generalized polylogarithm

Deepshikha Mishra, A. Swaminathan

The purpose of this manuscript is to derive two distinct integral representations of the generalized polylogarithm using two different techniques. The first approach involves the D…

math.CV2019

Starlike And Convex Functions Associated with A Nephroid domain having Cusps On The Real Axis

Lateef Ahmad Wani, A. Swaminathan

In this paper, we show that the Carathéodory function $φ_{N e} (z) = 1 + z - z^{3} /3$ maps the open unit disk $D$ onto the interior of the nephroid, a $2$ -cuspe…

math.CV2019

Radius Problems For Functions Associated with a Nephroid Domai

Lateef Ahmad Wani, A. Swaminathan

Let $S_{N e}^{*}$ be the collection of all analytic functions $f (z)$ defined on the open unit disk $D$ and satisfying the normalizations $f (0) = f^{'} (0) - 1 = 0$ such that…

math.CV2019

Differential Subordinations for Starlike Functions Associated With A Nephroid Domain

Lateef Ahmad Wani, A. Swaminathan

Let $A$ be the set of all analytic functions $f$ defined in the open unit disk $D$ and satisfying $f (0) = f^{'} (0) - 1 = 0$ . In this paper, we consider the function $φ_{\…

math.CV2019

Sufficient Conditions and Radius Problems for a starlike Class Involving a Differential Inequality

Lateef Ahmad Wani, A. Swaminathan

Let $A_{n}$ be the class of analytic functions $f (z)$ of the form $f (z) = z + \sum_{k = n + 1}^{\infty} a_{k} z^{k}, n \in N$ and let \begin{align*} Ω_n:=\left\{f\in\mathcal{A}_n:\l…

math.CV2018

On a conjecture for trigonometric sums by S. Koumandos and S. Ruscheweyh

Priyanka Sangal, A. Swaminathan

S. Koumandos and S. Ruscheweyh posed the following conjecture: For $ρ \in (0, 1]$ and $0 < μ \leq μ^{*} (ρ)$ , the partial sum $s_{n}^{μ} (z) = k = 0 \sum n \frac{( μ ) _{k}}{k !} z^{k}$ , $…