On a Certain Nonlinear Differential Monomial Sharing a Nonzero Polynomial

With the idea of normal family, we study the uniqueness of meromorphic functions f and g in the case where fn(ℒ(f))m − p and gn(ℒ(g))m − p share two values; here, ℒ(f) = akf(k) + ak−1f(k−1) + . . .+a1f’ +a0f, ak(6= 0),ak−1, . . . ,a1,a0 ∈ ℂ, and p(z)(6≢ 0) is a polynomial. The obtained result significantly improves and generalizes the result obtained by A. Banerjee and S. Majumder in [Bol. Soc. Mat. Mex. (2016); https://doi.org/10.1007/s40590-016-0156-0 ].