Abstract
In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree <TEX>$\bar{d}$</TEX>(P) and lower degree <TEX>$\underline{d}$</TEX>(P).
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