3 citations · 5 across the 19 of their papers we have counts for
23 papers
A Zalcman-Pang type rescaling result for -normal harmonic mappings and applications
Kuldeep Singh Charak, Pratiksha, Nikhil Bharti
We investigate normality and -normality criteria for harmonic mappings in the unit disk. A new sufficient condition for normality involving extended spherical derivatives is est…
Normality criterion for a family of holomorphic curves that partially share wandering hyperplanes with their derivatives, and holomorphic functions lifted to curves in
Sonam Mehta, Kuldeep Singh Charak
In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in . Further we obtain a normality criterion for f…
Value distribution of certain differential polynomials leading to some normality criteria
Kuldeep Singh Charak, Nikhil Bharti
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 re…
Normality through partial sharing of sets with differential polynomials
Kuldeep Singh Charak, Nikhil Bharti, Anil Singh
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,…
Counterexamples to Bloch's Principle and its Converse in Several Complex Variables
Kuldeep Singh Charak, Rahul Kumar
In this paper, besides a counterexample to Bloch's principle, normality criteria leading to counterexamples to the converse of Bloch's principle in several complex variables are pr…
Normality through sharing of pairs of functions with derivatives
Kuldeep Singh Charak, Manish Kumar, Anil Singh
Let and let and be three distinct complex numbers. If, there exist a holomorphic function on and a positive constant such…
Normality from one family of meromorphic functions to another through sharing of values
Kuldeep Singh Charak, Manish Kumar, Rahul Kumar
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 th…
Some variations on an extension of Caratheodory's normality criterion
Kuldeep Singh Charak, Rahul Kumar
In this note we give some variations on an extension of Caratheodory's normality criterion due to Grahl and Nevo.
Fatou and Julia like sets II
Kuldeep Singh Charak, Anil Singh, Manish Kumar
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 ge…
Fatou and Julia like sets
Kuldeep Singh Charak, Anil Singh, Manish Kumar
For a family of holomorphic functions on an arbitrary domain, we introduce Fatou and Julia like sets, and establish some of their interesting properties.
Some Normality Criteria for Families of Holomorphic Functions of Several Complex Variables
Kuldeep Singh Charak, Rahul Kumar
We prove a Zalcman-Pang lemma in several complex variables and apply it to obtain several complex variables analogues of the known normality criteria like Lappan's five-point theor…
Primeness and dynamics of some classes of entire functions
Kuldeep Singh Charak, Manish Kumar, Anil Singh
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 func…
A value distribution result related to Hayman's alternative
Kuldeep Singh Charak, Anil Singh
Motivated by Bloch's principle, we prove a value distribution result for meromorphic functions which is related to Hayman's alternative in certain sense.
Uniqueness of differential polynomials sharing one value
Kuldeep Singh Charak, Banarsi Lal
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…
A normality criterion generalizing Gu's result
Kuldeep Singh Charak, Virender Singh
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 no…
Some Normality Criteria and a Counterexample to the Converse of Bloch's Principle
Kuldeep Singh Charak, Shittal Sharma
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 normal…
Sharing of a set of meromorphic functions and Montel's theorem
Kuldeep Singh Charak, Virender Singh
In this paper we prove the result: Let be a family of meromorphic functions on a domain such that every pair of members of shares a set $S:=\left\{ψ…
Normality criteria concerning composite meromorphic functions
Virender Singh, Kuldeep Singh Charak
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…
Uniqueness of p(f) and P[f]
Kuldeep Singh Charak, Banarsi Lal
Let f be a non constant meromorphic function and a(not identically zero or infinity) be a meromorphic function satisfying T(r,a) = o(T(r,f)) as r tends to infinity, and p(z) be a p…
Two normality criteria and counterexamples to the converse of the bloch's principle
Kuldeep Singh Charak, Virender Singh
In this paper, we prove two normality criteria for a family of meromorphic functions. The first criterion extends a result of Fang and Zalcman[Normal families and shared values of…
Infinite Dimensional Bicomplex Spectral Decomposition Theorem
Kuldeep Singh Charak, Ravinder Kumar, Dominic Rochon
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operator…
Bicomplex Riesz-Fischer Theorem
K. S. Charak, R. Kumar, D. Rochon
This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in previous articles on the topic. Besides obtaining a Best Approximation Theorem, the ma…
Normal Families of Bicomplex Meromorphic Functions
K. S. Charak, D. Rochon, N. Sharma
In the present paper, we introduced the extended bicomplex plane , its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enable…