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MEROMORPHIC FUNCTION PARTIALLY SHARES SMALL FUNCTIONS OR VALUES WITH ITS LINEAR c-SHIFT OPERATOR
Banerjee, Abhijit,Maity, Sayantan Korean Mathematical Society 2021 대한수학회보 Vol.58 No.5
In this paper, we have studied on the uniqueness problems of meromorphic functions with its linear c-shift operator in the light of partial sharing. Our two results improve and generalize two very recent results of Noulorvang-Pham [Bull. Korean Math. Soc. 57 (2020), no. 5, 1083-1094] in some sense. In addition, our other results have improved and generalized a series of results due to Lü-Lü [Comput. Methods Funct. Theo. 17 (2017), no. 3, 395-403], Zhen [J. Contemp. Math. Anal. 54 (2019), no. 5, 296-301] and Banerjee-Bhattacharyya [Adv. Differ. Equ. 509 (2019), 1-23]. We have exhibited a number of examples to show that some conditions used in our results are essential.
ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WHEN TWO DIFFERENTIAL MONOMIALS SHARE ONE VALUE
Banerjee, Abhijit Korean Mathematical Society 2007 대한수학회보 Vol.44 No.4
We prove four theorems on the uniqueness of non linear differential polynomials sharing one value which improve a result of Yang and Hua, and supplements some results of Lahiri, Xu and Qiu and Banerjee.
Abhijit Banerjee,Arpita Kundu 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its $k$-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity \cite{Ban-Maity_Contemp.}.
Uniqueness of Meromorphic Functions Sharing a Small Function with Their Differential Polynomials
Banerjee, Abhijit Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.4
With the aid of weakly weighted sharing and a recently introduced sharing notion in [3] known as relaxed weighted sharing we investigate the uniqueness of meromorphic functions sharing a small function with its differential polynomials. Our results will improve and supplement all the results obtained by Zhang and Yang [17] as well as a substantial part of the results recently obtained by the present author [2] and thus provide a better answer to the questions posed by Yu [14] in this regard.
Certain Nonlinear Differential Polynomials Sharing a Nonzero Polynomial with Finite Weight
BANERJEE, ABHIJIT,SAHOO, PULAK Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.3
With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author.
Uniqueness of Meromorphic Functions That Share Three Sets
Banerjee, Abhijit Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
Dealing with a question of gross, we prove some uniqueness theorems concerning meromorphic functions with the notion of weighted sharing of sets. Our results will not only improve and supplement respectively two results of Lahiri-Banerjee [9] and Qiu and Fang [13] but also improve a very recent result of the present author [1].
Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points
Banerjee, Abhijit Department of Mathematics 2011 Kyungpook mathematical journal Vol.51 No.1
Using the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain non-linear differential polynomials share the same 1-points. Though the main concern of the paper is to improve a result of Fang [5] but as a consequence of the main result we improve and supplement some former results of Lahiri-Sarkar [16], Fang-Fang[6] et. al.
On uniqueness of meromorphic functions when two differential monomials share one value
Abhijit Banerjee 대한수학회 2007 대한수학회보 Vol.44 No.4
We prove four theorems on the uniqueness of non linear dif-ferential polynomials sharing one value which improve a result of Yangand Hua, and supplements some results of Lahiri, Xu and Qiu and Baner-jee.
ON TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS
Banerjee, Abhijit,Biswas, Tania,Maity, Sayantan Korean Mathematical Society 2022 대한수학회보 Vol.59 No.5
In this paper, for a transcendental meromorphic function f and α ∈ ℂ, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: $$f^n+{\alpha}f^{n-2}f^{\prime}+P_d(z,f)={\sum\limits_{i=1}^{k}}{p_i(z)e^{{\alpha}_i(z)},$$ where P<sub>d</sub>(z, f) is a differential polynomial of f, p<sub>i</sub>'s and α<sub>i</sub>'s are non-vanishing rational functions and non-constant polynomials, respectively. When α = 0, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case α ≠ 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.
ON THE GENERALIZATIONS OF BRÜCK CONJECTURE
Banerjee, Abhijit,Chakraborty, Bikash Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
We obtain similar types of conclusions as that of $Br{\ddot{u}}ck$ [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover a number of examples have been exhibited to justify the necessity or sharpness of some conditions used in the paper. At last we pose an open problem for future research.