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 f(n)(Script capital L(f))(m)- p and g(n)(Script capital L(g))(m)- p share two values; here, Script capital L(f) = a(k)f((k)) + a(k-1)f((k-1)) + . . .+a(1)f(') +a(0)f, a(k)(6= 0),a(k-1), . . . ,a(1),a(0)is an element of Double-struck capital C, and p(z)(6 not equivalent to 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); ].