On certain non-linear differential monomial sharing non-zero polynomial

S. Majumder; A. Dam

doi:10.37863/umzh.v73i2.99

S. Majumder Raiganj Univ., West Bengal, India
A. Dam North Bengal St. Xavier’s College, West Bengal, India

DOI: https://doi.org/10.37863/umzh.v73i2.99

Keywords: Uniqueness, Meromorphic function, small functions, Non-linear differential polynomials and normal family

Abstract

UDC 517.5

With the idea of normal family we study the uniqueness of meromorphic functions $f$ and $g$ when $f^{n}(\mathcal{L}(f))^{m}-p$ and $g^{n}(\mathcal{L}(g))^{m}-p$ share two values, where $\mathcal{L}(f)= a_{k}f^{(k)}+a_{k-1} f^{(k-1)}+\ldots+a_{1} f'+a_{0}f,$ $a_{k}(\ne 0),a_{k-1},\ldots,a_{1},a_{0}\in\mathbb{C}$ and $p(z)(\not\equiv 0)$ is a polynomial. The obtained result significantly improves and generalizes the result in [A. Banerjee, S. Majumder, On certain non-linear differential polynomial sharing a non-zero polynomial, Bol. Soc. Mat. Mex. (2016),https://doi.org/10.1007/s40590-016-0156-0].

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