arXiv subjects

Prachi Prajna Dash

Publications and source records attributed to Prachi Prajna Dash.

3 recordsLinked to original sources

arXiv2024

Radii for sections of functions convex in one direction

Let $\mathcal{G}(α)$ denote the family of functions $ f(z)$ in the open unit disk $\mathbb D :=\{z\in\mathbb{C}: |z|<1\}$ that satisfy $ f(0)=0= f'(0)=1$ and \[\Re \left(1+ \dfrac{z f''(z)}{ f'(z)}\right)<1+\dfracα{2} , \quad z\in \mathbb D.\] We determine the disks $|z|<ρ_n$ in which sections $ s_n(z; f)$ of $ f(z)$ are convex, starlike, and close-to-convex of order $β\;(0\le β< 1)$. Further, we obtain certain inequalities of sections in the considered class of functions.

math.CV↗

arXiv2024

On certain analytic functions defined by differential inequality

For the family of analytic functions $f(z)$ in the open unit disk $\mathbb{D}$ with $f(0)=f'(0)-1=0$, satisfying the differential equation \begin{equation*} zf'(z) - f(z) = \dfrac{1}{2} z^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} we obtain radii of convexity, starlikeness, and close-to-convexity of partial sums of $f(z)$. We also study the generalization of this family having the form \begin{equation*} zf'(z)-f(z) = λz^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} where $λ> 0,$ and obtain some useful properties of these functions.

math.CV↗

arXiv2024

Certain subclass of harmonic functions associated with univalent functions

In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain some characteristic properties, including radius properties, convolution, coefficient estimates and their properties, growth estimates, and convex combination for the functions in the defined subclass. At last, we produce conditions for some special functions as well as harmonic univalent polynomials to belong to the defined subclass of harmonic functions.

math.CV↗