7 citations · 18 across the 15 of their papers we have counts for
19 papers
On -Normality of Harmonic Mappings and Their Families
Gopal Datt, Ritesh Pal
In this paper, we present Lappan's five-point type criteria for -normality of sense-preserving harmonic mappings and families of harmonic mappings in the unit disc .…
A Function-Sharing Criterion for Normal Functions
Gopal Datt, Ritesh Pal, Ashish Kumar Trivedi
In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let be a meromorphic function in the unit disc …
Dynamics of complex harmonic mappings
Gopal Datt, Ramanpreet Kaur
This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some co…
Normal Families of Holomorphic Curves and Sharing of Moving Hyperplanes Wandering on
Gopal Datt, Naveen Gupta, Nikhil Khanna +1
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 . We…
Lappan's five-point theorem for ϕ-Normal Harmonic Mappings
Nisha Bohra, Gopal Datt, Ritesh Pal
A harmonic mapping in is -normal if where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.…
Ascent and Descent of Weighted Composition Operators on Lorentz spaces
Gopal Datt, Daljeet Singh Bajaj
The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation …
Improvements to the Montel-Carathéodory Theorem for families of -valued holomorphic curves
Gopal Datt
In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain into to be normal. Our results are…
Normality and Montel's Theorem
Gopal Datt, Sanjay Kumar
In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the me…
A normality Criterion for a Family of Meromorphic Functions
Gopal Datt, Sanjay Kumar
Schwick, in [6], states that let be a family of meromorphic functions on a domain and if for each , , for , where $n,…
Meromorphically normal families and a meromorphic Montel-Carathéodory theorem
Gopal Datt
In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain into to be meromorphically normal. M…
Quasi-normal families of meromorphic mappings sharing hypersurfaces
Gopal Datt
In this article we prove a sufficient condition of quasi-normality in higher dimension for a family of meromorphic mappings in which each pair of functions of family shares some mo…
Quasi-normality and Shared Functions
Gopal Datt
We prove two sufficient conditions of quasi-normality in which each pair and of shares some holomorphic functions.
A Criterion for quasi normality in
Gopal Datt, Sanjay Kumar
In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in that takes values in a comp…
On a Theorem of Schwick
Gopal Datt, Sanjay Kumar
Let D be a domain, n, k be positive integers and n >= K+3. Let F be a family of functions meromorphic in D. If each f in F satisfies (f^n)^(k) not equal to 1 for z in D, then F is…
Some Normality Criteria
Gopal Datt, Sanjay Kumar
In this article we prove some normality criteria for a family of meromorphic functions which involves sharing of a non-zero value by certain differential monomials generated by the…
Normality and Sharing Functions
Gopal Datt, Sanjay Kumar
In this article, we prove a normality criterion for a family of meromorphic functions which involves sharing of holomorphic functions. Our result generalizes some of the results of…
Normality criteria for a family of meromorphic functions with multiple zeros
Gopal Datt, Yuntong Li, Poonam Rani
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic funct…
Normality and Sharing Values
Gopal Datt, Sanjay Kumar Pant
In this paper, we obtained some normality criteria for families of holomorphic functions. Which generalizes some results of Fang, Xu, Chen and Hua.
Dynamics of composite entire functions
Dinesh Kumar, Gopal Datt, Sanjay Kumar Pant
It is known that the dynamics of and vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the e…