Abstract
Let be an analytic function on the unit disc
with image satisfying a measure condition. We prove an upper and a lower bound for the modulus
for every
involving all the pre-images of
Acknowledgements
The first-named author would like to thank the Cyprus State Scholarship Foundation for its support. The content of the paper was carried out while the second-named author was a postdoctoral associate of University of Cyprus. The authors would like to thank the referee for his remarks and especially for his suggestion to compare their result with a theorem of Mityuk [Citation12].