Title of article :
On Maximum Modulus of Polynomials with Restricted Zeros
Author/Authors :
Chanam ، Barchand Department of Mathematics - Faculty of Science - National Institute of Technology Manipur , Devi ، Khangembam Babina Department of Mathematics - Faculty of Science - National Institute of Technology Manipur , Krishnadas ، Kshetrimayum Department of Mathematics - Faculty of Science - Shaheed Bhagat Singh College (University of Delhi) , Devi ، Maisnam Triveni Department of Mathematics - Faculty of Science - National Institute of Technology Manipur
Abstract :
Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros in |z| ≥ k or in |z| ≤ k, k 0. In this paper, firstwe obtain inequalities about the dependence of |p(Rz)| on |p(rz)|, where |z| = 1, for r 2 ≤ Rr ≤ k2 or k2 ≤ Rr ≤ R2. Further, another similar inequality for the class of polynomials having all zeros in |z| ≥ k, k 0 is also proved for 0 r ≤ R ≤ k. Our results improve as well as generalize certain well-known polynomial inequalities.
Keywords :
Polynomial , Zeros , Inequalities , Maximum modulus
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
