arrow
Volume 33, Issue 1
Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial

A. Mir, M. Bidkham & B. Dar

Anal. Theory Appl., 33 (2017), pp. 1-10.

Published online: 2017-01

Export citation
  • Abstract

In this paper, we consider an operator $D_α$ which maps a polynomial $P(z)$ in to $D_αP(z):= np(z)+(α−z)P′(z)$, where $α ∈ \mathcal{C}$ and obtain some $L^{\gamma}$ inequalities for lucanary polynomials having zeros in $|z|≤k≤1$. Our results yields several generalizations and refinements of many known results and also provide an alternative proof of a result due to Dewan et al. [7], which is independent of Laguerre’s theorem.

  • AMS Subject Headings

30A10, 30C10, 30C15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{ATA-33-1, author = {A. Mir, M. Bidkham and B. Dar}, title = {Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {1}, pages = {1--10}, abstract = {

In this paper, we consider an operator $D_α$ which maps a polynomial $P(z)$ in to $D_αP(z):= np(z)+(α−z)P′(z)$, where $α ∈ \mathcal{C}$ and obtain some $L^{\gamma}$ inequalities for lucanary polynomials having zeros in $|z|≤k≤1$. Our results yields several generalizations and refinements of many known results and also provide an alternative proof of a result due to Dewan et al. [7], which is independent of Laguerre’s theorem.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n1.1}, url = {http://global-sci.org/intro/article_detail/ata/4611.html} }
TY - JOUR T1 - Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial AU - A. Mir, M. Bidkham & B. Dar JO - Analysis in Theory and Applications VL - 1 SP - 1 EP - 10 PY - 2017 DA - 2017/01 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n1.1 UR - https://global-sci.org/intro/article_detail/ata/4611.html KW - Polar derivative, polynomials, $L^{\gamma}$-inequalities in the complex domain, Laguerre's theorem. AB -

In this paper, we consider an operator $D_α$ which maps a polynomial $P(z)$ in to $D_αP(z):= np(z)+(α−z)P′(z)$, where $α ∈ \mathcal{C}$ and obtain some $L^{\gamma}$ inequalities for lucanary polynomials having zeros in $|z|≤k≤1$. Our results yields several generalizations and refinements of many known results and also provide an alternative proof of a result due to Dewan et al. [7], which is independent of Laguerre’s theorem.

A. Mir, M. Bidkham and B. Dar. (2017). Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial. Analysis in Theory and Applications. 33 (1). 1-10. doi:10.4208/ata.2017.v33.n1.1
Copy to clipboard
The citation has been copied to your clipboard