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Kuldeep Singh Charak

Publications and source records attributed to Kuldeep Singh Charak.

At least 19 recordsLinked to original sources
arXiv2026

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

We investigate normality and $ϕ$-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 $ϕ$-normal harmonic mappings and derive new $ϕ$-normality criteria as applications. In addition, we introduce $ϕ$-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↗
arXiv2024

Normality criterion for a family of holomorphic curves that partially share wandering hyperplanes with their derivatives, and holomorphic functions lifted to curves in $P^2(\mathbb{C})$

In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share wandering holomorphic functions with their derivatives. We also devise a tractable representation of complex valued holomorphic functions from D as functions from D to $P^2(\mathbb{C})$ obtain a normality criterion that leads to a counterexample to the converse of Bloch's principle.

math.CV↗
arXiv2023

Value distribution of certain differential polynomials leading to some normality criteria

In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for certain differential polynomials which lead to some normality criteria involving sharing of holomorphic functions with certain differential polynomials. As a consequence, a counterexample to the converse of the Bloch's principle is also given.

math.CV↗
arXiv2022

Normality through partial sharing of sets with differential polynomials

This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are also established which improve and generalize many known results.

math.CV↗
arXiv2022

Normality through sharing of pairs of functions with derivatives

Let $\mathcal{F}\subset\mathcal{M}(D)$ and let $a, b$ and $c$ be three distinct complex numbers. If, there exist a holomorphic function $h$ on $D$ and a positive constant $ρ$ such that for each $f\in\mathcal{F},$ $f$ and $f^{'}$ partially share three pairs of functions $(a,h), \ (b, c_f)$ and $(c,d_f)$ on $D,$ where $c_f$ and $d_f$ are some values in some punctured disk $D^*_ρ(0),$ then $\mathcal{F}$ is normal in $D$. This is an improvement of Schwick's result[Arch. Math. (Basel), \textbf{59} (1992), 50-54]. We also obtain several normality criteria which significantly improve the existing results and examples are given to establish the sharpness of results.

math.CV↗
arXiv2021

Normality from one family of meromorphic functions to another through sharing of values

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f in F, there exists g in G such that f and g share a, b and c partially, then F is normal in D. This gives a sharp improvement of a result due to X. J. Liu, S. H. Li and X. C. Pang. We also prove some interesting related sharp results.

math.CV↗
arXiv2020

Fatou and Julia like sets II

This paper is a continuation of authors work: Fatou and Julia like sets,Ukranian J. Math., to appear/arXiv:2006.08308[math.CV](see [4]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic functions on an arbitrary domain, and establish some distinctive properties of these sets. The connectedness of the Julia like set is also proved.

math.CV↗
arXiv2020

Fatou and Julia like sets

For a family of holomorphic functions on an arbitrary domain, we introduce Fatou and Julia like sets, and establish some of their interesting properties.

math.CV↗
arXiv2019

Primeness and dynamics of some classes of entire functions

In this paper we investigate the primeness of a class of entire functions and discuss the dynamics of a periodic member f of this class with respect to a transcendental entire function g that permutes with f. In particular we show that the Julia sets of f and g are identical.

math.CV↗
arXiv2016

Uniqueness of differential polynomials sharing one value

We prove some uniqueness results which improve and generalize results of Jiang-Tao Li and Ping Li[Uniqueness of entire functions concerning differential polynomials. Commun. Korean Math. Soc. 30 (2015), No. 2, pp. 93-101].

math.CV↗
arXiv2016

A normality criterion generalizing Gu's result

In this paper we prove a normality criterion for the families of meromorphic functions involving sharing of functions. Our result generalizes some of the earlier results on Gu's normality criterion.

math.CV↗
arXiv2015

Some Normality Criteria and a Counterexample to the Converse of Bloch's Principle

In this paper we continue our earlier investigations on normal families of meromorphic functions\cite{CS2}. Here, we prove some value distribution results which lead to some normality criteria for a family of meromorphic functions involving the sharing of a holomorphic function by more general differential polynomials generated by members of the family and get some recently known results extended and improved. In particular, the main result of this paper leads to a counterexample to the converse of Bloch's principle.

math.CV↗
arXiv2015

Sharing of a set of meromorphic functions and Montel's theorem

In this paper we prove the result: Let $\mathcal{F}$ be a family of meromorphic functions on a domain $Ω$ such that every pair of members of $\mathcal{F}$ shares a set $S:=\left\{ψ_1(z), ψ_2(z), ψ_3(z) \right\}$ in $Ω$, where $ψ_j(z), \ j=1,2,3$ is meromorphic in $Ω.$ If for every $f\in \mathcal{F}$, $f(z_0)\neq ψ_i (z_0)$ whenever $ψ_i(z_0)=ψ_j(z_0)$ for $i,j\in \left\{1,2,3 \right\}(i\neq j)$ and $z_0\in Ω,$ then $\mathcal{F}$ is normal in $Ω$. This result generalizes a result of M.Fang and W.Hong [Some results on normal family of meromorphic functions, Bull. Malays. Math. Sci. Soc. (2)23 (2000),143-151,] and in particular, it generalizes the most celebrated theorem of Montel-the Montel's theorem.

math.CV↗
arXiv2015

Normality criteria concerning composite meromorphic functions

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors carried out in recent years.

math.CV↗