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ON EXTREMAL PROPERTIES FOR THE POLAR DERIVATIVE OF POLYNOMIALS.pdf
Ana1．Theory App1．
Vo1．27，No．2(2011)，150-157
DOI10．1007／s10496．011-01503
ON EXTREMAL PROPERTIESFOR
THEPOLAR DERIVATIVE OFPOLYNOM IALS
K．K．Dewan and Arty~auja
(NaturalSciencesJamiaMilliaIslamia，CentralUniersityIndinJ
,
ReceivedJune23，2010
⑥Edi。rialB。ard。fAnalysisinThe。ryApplicati。nsandSpringer-VerlagBerlinHeidelberg20ll
Abstrac：‘Ifp(z)isapolynomialofdegreenhavingallitszeroson =七七 I，t}lenit
，
，
iSprovedi，jmat
m axIP，(z)l而 ,／／臀 )1．
IzJ=l
Inthispape~wegeneralizetheaboveinequalitybyextendingittohtepolardeftvati
veOfa
polynomialofhtetype (z)=cn +∑ ～J_。，1 ．“ ．Wealsoobtaincertainnew
mequalitiesconcerningthemaximum modulusofapolynomialwiht restrictedzems
．
Keywords：polynomial,zerosinequality,polarderiv日tivP
，
AMS(2010)subjectclassification：30A10，30C10，30C15
1 Introduction
Ifp(z)isapolynomialofdegree，zandp(z)itsderivative，thenaccordingtoafamousresu1t
knownasBernstein’Sinequality(forreferencesee2【】)wehave
，
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