arXiv subjects

Ritesh Pal

Publications and source records attributed to Ritesh Pal.

3 recordsLinked to original sources

arXiv2025

A Function-Sharing Criterion for Normal Functions

In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let $f$ be a meromorphic function in the unit disc $\mathbb{D}\subset \mathbb{C}$, $\psi_1$, $\psi_2$, and $\psi_3$ be three meromorphic functions in the unit disc $\mathbb{D}$, continuous on $ \partial{\mathbb{D}}:=\{z\in\mathbb{C}\,:\,|z|=1\}$, such that $\psi_i(z)\neq\psi_j(z)$ $(1\leq i<j\leq 3)$ $\partial\mathbb{D}$. We prove that, if $\psi_1$, $\psi_2$, and $\psi_3$ share the function $f$ on $\mathbb{D}$, then $f$ is normal. Building upon this, we further establish an additional criterion for normal functions.

math.CV↗

arXiv2024

Normal Families of Holomorphic Curves and Sharing of Moving Hyperplanes Wandering on $\mathbb{P}^n$

In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on the respective holomorphic curve in the family under consideration), and establish a sufficient condition of normality concerning shared hyperplanes.

math.CV↗

arXiv2024

Lappan's five-point theorem for {\phi}-Normal Harmonic Mappings

A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $\varphi$-normal if $f^{\#}(z)=\mathcal{O}(|\varphi(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $\varphi$-normal. We also extend the five-point theorem of Lappan for $\varphi$-normal harmonic mappings.

math.CV↗