Volume 29, Issue 4
New Inequalities on Lγ-Spaces

Abdullah Mir, Bilal Dar & Sajad Amin Baba

Anal. Theory Appl., 29 (2013), pp. 390-400.

Published online: 2013-11

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  • Abstract

We consider for a fixed µ, the class of polynomials Pn,µ,s := n P(z) =z s  anz n−s+ n−s ∑ j=µ an−jz n−j−s  ; 1≤µ≤n−s o of degree n, having all zeros in |z|≤k, k≤1, with s-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

  • Keywords

Polynomial Zygmund inequality polar derivative

  • AMS Subject Headings

30A10 30C10 30D15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-29-390, author = {Abdullah Mir, Bilal Dar and Sajad Amin Baba}, title = {New Inequalities on Lγ-Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {4}, pages = {390--400}, abstract = {

We consider for a fixed µ, the class of polynomials Pn,µ,s := n P(z) =z s  anz n−s+ n−s ∑ j=µ an−jz n−j−s  ; 1≤µ≤n−s o of degree n, having all zeros in |z|≤k, k≤1, with s-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n4.8}, url = {http://global-sci.org/intro/article_detail/ata/4533.html} }
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