Abhijit Banerjee

Weighted sharing of a small function by a meromorphic function and its derivative

The paper deals with the problem of meromorphic functions sharing a small function with its derivative and improves the results of Yu [K.W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4 (1) (2003) Art. 21 (Online: http://jipam.vu.edu.au/)], Lahiri-Sarkar [I. Lahiri, A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (1) (2004) Art. 20 (Online: http://jipam.vu.edu.au/)] and a recent result of Zhang [Q.C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (4) (2005) Art. 116 (Online: http://jipam.vu.edu.au/)].

Uniqueness of Meromorphic Functions That Share Three Sets

In the paper we prove some results related to the uniqueness of meromorphic as well as entire functions. Our results will improve and supplement several known results .

Further investigations on a question of Zhang and Lü

Abstract In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points

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.

Uniqueness of meromorphic functions sharing three sets – Further study

Abstract The notion of weighted sharing of sets is employed to deal with the problem of uniqueness of meromorphic functions sharing three sets. We obtain two results which radically improve and extend a number of results in [2] and [3].

Uniqueness of Meromorphic Functions Sharing a Small Function with Their Differential Polynomials

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.

Tumura–Clunie Theorem Concerning Differential Polynomials

In this article we prove Tumura–Clunie type theorems which improve some earlier results and as consequences of the main results we extend a theorem of Hayman.

Uniqueness properties of meromorphic functions in the light of three shared sets

Abstract We use the notion of weighted sharing of sets to improve a number of results in the uniqueness theory of meromorphic functions sharing three sets. We have also presented a new idea in the formation of one of the range sets in connection with the three shared set problems, which ultimately yields a better result than many existing result in some sense.

On the Uniqueness of Power of a Meromorphic Function Sharing a set with its k-Th Derivative

In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing

Further results on uniqueness of derivatives of meromorphic functions sharing three sets

In this paper we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.