arXiv subjects

Pratiksha

Publications and source records attributed to Pratiksha.

2 recordsLinked to original sources

arXiv2026

On normality and $\varphi$-normality of holomorphic functions in several complex variables

In this paper, we investigate $\varphi$-normal functions and normal families of holomorphic functions concerning total derivatives in $\mathbb{C}^{n}.$ More precisely, we prove a sufficient condition for a holomorphic function defined on an open unit ball in $\mathbb{C}^{n}$ satisfying certain conditions involving higher order partial derivatives to be $\varphi$-normal. Furthermore, by using differential inequalities involving total differential polynomials in $\mathbb{C}^{n}$, we establish some normality criteria for holomorphic functions in $\mathbb{C}^{n}$ which generalize some known results.

math.CV↗

arXiv2026

A Zalcman-Pang type rescaling result for $\phi$-normal harmonic mappings and applications

We investigate normality and $\phi$-normality criteria for harmonic mappings in the unit disk. A new sufficient condition for normality involving extended spherical derivatives is established. We further prove a Zalcman-Pang type rescaling lemma for $\phi$-normal harmonic mappings and derive new $\phi$-normality criteria as applications. In addition, we introduce $\phi$-normal families of harmonic mappings and obtain corresponding Lappan-type characterizations. In particular, we show that for sense-preserving harmonic mappings the relevant test set may be taken to consist of only three points.

math.CV↗