For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...

‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

In this paper, we present a correct proof of an L p-inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

We derive iterative methods for computing the Fréchet derivative of the map which 6 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 7 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 8 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 9 identity that relates the ...

1. Reaction of 2-(N-acetoxy)-acetamidofluorene with orthophosphate buffer at pH7 yielded a large quantity of water-soluble fluorene derivatives, which showed absorption peaks at 303, 290 and 280nm. Tris buffer under similar conditions gave negligible reaction. 2. Hydrolysis of polar material with acid or alkaline phosphatases liberated equimolar amounts of inorganic phosphate and an ether-extra...

If is a polynomial of degree n such that in , then Govil [ Proc. Nat. Acad. Sci., Vol. 50, pp. 50-52, 1980. ] proved &#x0D; provided and attain their maxima at the same point on circle where .&#x0D; Equality above inequality holds for.&#x0D; In this paper, we extend an improved version into polar derivative polynomial.