Abstract
Letp(z)beapolynomial of degreen,withp(z)= n ν=0 aνzν. Inthis paper,firstly,weprovearesultforboundsintwodifferentradii forthemaximum modulusof lacunarytypeofpolynomialshavingall zerosoutsideadiskofgiven radius. Next,we establisha result concerning themaximummodulus of polar derivativeof polynomial havingall zeros insideadiskout ofwhichsomefixed numberof zerosarecentredatorigin. Inparticularcasethis result reduces into ordinaryderivative.Ourresultsnotonlyproviderefinementsofearlierprovedresultsbutalsoopennewavenuesforotherresultsinthesamefieldofresearch.
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