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IMCS/Publications/BASM/Issues/BASM n.3(82), 2016/

Uniqueness of certain power of a meromorphic function sharing a set with its differential monomial

Authors: Abhijit Banerjee, Molla Basir Ahamed

Abstract

In this paper we are mainly devoted to find out the specific form of a meromorphic function when it shares a set of small functions with its differential monomial counterpart. Our results will improve and extend some of the recent results due to Zhang-Yang [J. L. Zhang and L. Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math. 34(2009), 249--260] and Xu-Yi-Yang [H. Y. Xu, C. F. Yi and H.~Wang, On a conjecture of R.~Bruck concerning meromorphic function sharing small functions, Revista de Matematica Teoria y Aplicaciones, 23(1)(2016), 291-308]. We provide some examples to show that certain conditions used in the paper can not be removed.

Abhijit Banerjee
Department of Mathematics
University of Kalyani
West Bengal 741235, India
E-mail: ,

Molla Basir Ahamed
Department of Mathematics
Kalipada Ghosh Tarai Mahavidyalaya
West Bengal 734014, India
E-mail: ,

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