Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

Abstract

Let fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}. The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.