On partial sums of certain meromophic pp-valent functions

In this paper, we study the ratio of meromorphic pp-valent functions in the punctured disk U∗={z:0<|z|<1}U∗={z:0<|z|<1} of the form f(z)=1zp+∑k=1∞ak+p−1zk+p−1 to its sequence of partial sums of the form f(z)=1zp+∑k=1n+p−1ak+p−1zk+p−1. Also, we determine sharp lower bounds for Re{f(z)/fn+p−1(z)},Re{fn+p−1(z)/f(z)},Re{f′(z)/fn+p−1′(z)} and Re{fn+p−1′(z)/f′(z)}.