In this paper, we establish various sufficient conditions for a family of holomorphic mappings on... more In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain $D\subseteq\mathbb{C}$ into $\mathbb{P}^n$ to be normal. Our results are improvements to the Montel-Carath\'eodory Theorem for a family of $\mathbb{P}^n$-valued holomorphic curves.
It is known that the dynamics of f and g vary to a large extent from that of its composite entire... more It is known that the dynamics of f and g vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions f and g having infinite number of domains satisfying various properties and relating it to their composition. We have explored and enlarged all the maximum possible ways of the solution in comparison to the past result worked out.
International Journal of Pure and Apllied Mathematics, 2014
In this paper, we obtain some normality criteria for families of holomorphic functions. these gen... more In this paper, we obtain some normality criteria for families of holomorphic functions. these generalize some results of Fang, Xu, Chen and Hua.
In this article, we give a Zalcman type renormalization result for the quasinormality of a family... more In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in Cn that takes values in a complete complex Hermitian manifold.
In this article we prove some normality criteria for a family of meromorphic functions which invo... more 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 members of the family. These result generalize some of the results of Schwick.
In this article, we prove a normality criterion for a family of meromorphic functions having zero... more 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 members of the family. Our result generalizes Montel's normality test in a certain sense.
Let D be a domain, n, k be positive integers and n ≥ k + 3. Let F be a family of functions meromo... more 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 ∈ F satisfies (f n) (k) (z) = 1 for z ∈ D, then F is a normal family. This result was proved by Schwick [10], in this paper we extend this theorem.
, states that let F be a family of meromorphic functions on a domain D and if for each f ∈ F , (f... more , states that let F be a family of meromorphic functions on a domain D and if for each f ∈ F , (f n ) (k) = 1, for z ∈ D, where n, k are positive integers such that n ≥ k + 3, then F is a normal family in D. In this paper, we investigate the opposite view that if for each has zeros in D, where ψ(z) is a holomorphic function in D, then what can be said about the normality of the family F ? 2010 Mathematics Subject Classification. 30D45.
Indian Journal of Pure and Applied Mathematics, 2015
In this article, we prove a normality criterion for a family of meromorphic functions which invol... more 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 H. H. Chen, M. L. Fang [3] and M. Han, Y. Gu [7].
In this article, we prove some normality criteria for a family of meromorphic functions having mu... more In this article, we prove some normality criteria for a family of meromorphic functions having multiple zeros and poles which involves sharing of a non-zero value by zeros and poles which involves a non linear differential polynomial.
We prove some normality criteria for families of meromorphic mappings of a domain D ⊂ C m into CP... more We prove some normality criteria for families of meromorphic mappings of a domain D ⊂ C m into CP n under a condition on the inverse images of moving hypersurfaces.
In this paper, we have shown that, by using results of Aladro and Krantz and of Fujimoto, Zalcman... more In this paper, we have shown that, by using results of Aladro and Krantz and of Fujimoto, Zalcman's type Lemma can be given for quasinormality of a family of holomorphic functions on a domain of $\mathbb{C}^n$ into a complete complex Hermitian manifold.
In this paper, we establish various sufficient conditions for a family of holomorphic mappings on... more In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain $D\subseteq\mathbb{C}$ into $\mathbb{P}^n$ to be normal. Our results are improvements to the Montel-Carath\'eodory Theorem for a family of $\mathbb{P}^n$-valued holomorphic curves.
It is known that the dynamics of f and g vary to a large extent from that of its composite entire... more It is known that the dynamics of f and g vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions f and g having infinite number of domains satisfying various properties and relating it to their composition. We have explored and enlarged all the maximum possible ways of the solution in comparison to the past result worked out.
International Journal of Pure and Apllied Mathematics, 2014
In this paper, we obtain some normality criteria for families of holomorphic functions. these gen... more In this paper, we obtain some normality criteria for families of holomorphic functions. these generalize some results of Fang, Xu, Chen and Hua.
In this article, we give a Zalcman type renormalization result for the quasinormality of a family... more In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in Cn that takes values in a complete complex Hermitian manifold.
In this article we prove some normality criteria for a family of meromorphic functions which invo... more 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 members of the family. These result generalize some of the results of Schwick.
In this article, we prove a normality criterion for a family of meromorphic functions having zero... more 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 members of the family. Our result generalizes Montel's normality test in a certain sense.
Let D be a domain, n, k be positive integers and n ≥ k + 3. Let F be a family of functions meromo... more 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 ∈ F satisfies (f n) (k) (z) = 1 for z ∈ D, then F is a normal family. This result was proved by Schwick [10], in this paper we extend this theorem.
, states that let F be a family of meromorphic functions on a domain D and if for each f ∈ F , (f... more , states that let F be a family of meromorphic functions on a domain D and if for each f ∈ F , (f n ) (k) = 1, for z ∈ D, where n, k are positive integers such that n ≥ k + 3, then F is a normal family in D. In this paper, we investigate the opposite view that if for each has zeros in D, where ψ(z) is a holomorphic function in D, then what can be said about the normality of the family F ? 2010 Mathematics Subject Classification. 30D45.
Indian Journal of Pure and Applied Mathematics, 2015
In this article, we prove a normality criterion for a family of meromorphic functions which invol... more 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 H. H. Chen, M. L. Fang [3] and M. Han, Y. Gu [7].
In this article, we prove some normality criteria for a family of meromorphic functions having mu... more In this article, we prove some normality criteria for a family of meromorphic functions having multiple zeros and poles which involves sharing of a non-zero value by zeros and poles which involves a non linear differential polynomial.
We prove some normality criteria for families of meromorphic mappings of a domain D ⊂ C m into CP... more We prove some normality criteria for families of meromorphic mappings of a domain D ⊂ C m into CP n under a condition on the inverse images of moving hypersurfaces.
In this paper, we have shown that, by using results of Aladro and Krantz and of Fujimoto, Zalcman... more In this paper, we have shown that, by using results of Aladro and Krantz and of Fujimoto, Zalcman's type Lemma can be given for quasinormality of a family of holomorphic functions on a domain of $\mathbb{C}^n$ into a complete complex Hermitian manifold.
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