A generalization of Livingston's coefficient inequalities for functions with positive real part

Some properties of analytic functions related with bounded positive real part

In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.

Harmonic Functions with Positive Real Part

In this paper, the class of harmonic functions f = h+ ḡ with positive real part and normalized by f(ζ) = 1, (|ζ| < 1) is studied, where h and g are analytic in U = {z : |z| < 1}. Some properties of this class are searched. Sharp coefficient relations are given for functions in this class. On the other hand, the author make use of Alexander integral transforms of certain analytic functions (whic...

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

Some numerical radius inequalities with positive definite functions

 ‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

Coefficient Inequalities for Certain Analytic Functions