A. Zireh
shahrood university of technology
[ 1 ] - On the polar derivative of a polynomial
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...
[ 2 ] - L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, |z|leq 1}$, for each $q>0$, the $|f|_{q}$ is defined as followsbegin{align*}begin{split}&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q}, 0
[ 3 ] - On the Linear Combinations of Slanted Half-Plane Harmonic Mappings
In this paper, the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.
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