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On the value distribution of differential polynomials
Subhas S. Bhoosnurmath,Milind Narayanrao Kulkarni,Kit-Wing Yu 대한수학회 2008 대한수학회보 Vol.45 No.3
In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree d (P) and lower degree d (P). In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree d (P) and lower degree d (P).
ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS
Bhoosnurmath, Subhas S.,Kulkarni, Milind Narayanrao,Yu, Kit-Wing Korean Mathematical Society 2008 대한수학회보 Vol.45 No.3
In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree $\bar{d}$(P) and lower degree $\underline{d}$(P).
A NOTE ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS
Bhoosnurmath, Subhas S.,Chakraborty, Bikash,Srivastava, Hari M. Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
Let f be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function T(r, f) in terms of the counting function of a homogeneous differential polynomial generated by f. Our result improves and generalizes some recent results.
WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS
Bhoosnurmath, Subhas S.,Pujari, Veena L. Korean Mathematical Society 2015 대한수학회보 Vol.52 No.1
In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.
WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS
SUBHAS S.BHOOSNURMATH,Veena L. Pujari 대한수학회 2015 대한수학회보 Vol.52 No.1
In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.
ON CHARACTERISTIC FUNCTION AND PROXIMATE DEFICIENCIES OF HOMOGENEOUS DIFFERENTIAL POLYNOMIALS
Waghamore,Bhoosnurmath 장전수학회 2009 Proceedings of the Jangjeon mathematical society Vol.12 No.3
In this paper relations between [수식] and T(r, P) have been obtained ,where p(r) is a proximate order relative to T(r, f) and P is a homogeneous dif- ferential polynomial respectively. Also results pertaining to Nevanlinna exceptional values have been established, and bounds for [수식] in terms of Nevanlinna de- fects have been given, where [수식] For instance it has been shown that if [수식] then, [수식]
On slowly changing function and multiple zeros of difference of two meromorphic functions
H. P. Waghamore,S. S. Bhoosnurmath 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.2
In this paper we compare the number of multiple zeros of f(z) − g(z) with the function rpK(r) where K(r) is a n- slowly changing function- satisfying K(cr) ∼ K(r) as r → ∞ for every fixed positive c.
RELATIVE DEFECTS AND MULTIPLE COMMON ROOTS OF TWO MEROMORPHIC FUNCTIONS
HARINA P. WAGHAMORE,SUBHAS S.BHOOSNURMATH 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
In this paper, we consider two different meromorphic functions having com-mon roots and and some relations involving the relative defects.
On exceptional values of homogeneous differential polynomials
H. P. Waghamore,S. S. Bhoosnurmath 장전수학회 2007 Proceedings of the Jangjeon mathematical society Vol.10 No.2
Let f be a meromorphic function of order , (0 < < 1). Let T(r, f) be the characteristic function of f(z). Let M(r, f) be the maximum of |f(z)| on |z| = r when f(z) is an entire function. For the function g(z) let n(r, 1/f −g) and ¯n(r, 1/f −g) be the number of zeros and the number of distinct zeros respectively of f(z)−g(z) in |z| r, where g is a small function of f i.e. T(r, g) = o(T(r, f)) = S(r, f).