REFINEMENTOFSOMEGENERALIZEDPOLYNOMIAL INEQUALITIES

Authors

  • Roshan Lal Keshtwal V.S.K.C.GovernmentPostgraduateCollege, Dakpathar,Dehradun-248125,Uttarakhand, INDIA
  • Susheel Kumar DepartmentofMathematics, DeshbandhuCollegeKalkaji,NewDelhi-110019, INDIA
  • Imran Ali DepartmentofMathematics, DharmanandUniyalGovernmentDegreeCollege, Narendranagar,TehriGarhwal-249175,Uttarakhand, INDIA

DOI:

https://doi.org/10.56827/SEAJMMS.2023.1902.08

Keywords:

Polynomials;Derivatives;PolarDerivative; Inequalities;MaximumModulus;Zeros.

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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Published

2023-08-30

Issue

Vol. 19 No. 02 (2023): South East Asian Journal of Mathematics and Mathematical Sciences

Section

Articles