Mahnaz Moradi Nargesi

• PhD
• Lecturer at California State University, Fullerton

For an analytic function f (z) = z+ ∞ n=2 a n z n satisfying the inequality ∞ n=2 n(n− 1)|a n | ≤ β, sharp bound on β is determined so that f is either starlike or convex of order α. Several other coefficient inequalities related to certain subclasses are also investigated.

Let $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ be analytic in the unit disk with second coefficient $a_2$ satisfying $|a_2|=2b$, $0\leq b\leq1$. Sharp radius of Janowski starlikeness and other radius constants are obtained when $|a_n|\leq cn+d$ ($c,d\geq0$) or $|a_n|\leq c/n$ ($c>0$) for $n\geq3$.

For lambda satisfying a certain admissibility criteria, sufficient conditions are obtained for the integral transform V(f)(z) := integral(1)(0)(t)f(tz)/tdt to map normalized analytic functions f satisfying Rce(i phi)(1 - alpha + 2 gamma)f(z)/2 + (alpha - 2 gamma)f'(z) + gamma zf ''(z) - beta) > 0 into the class of convex functions. Several interest...

For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated.

A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to be in certain subclasses of functions are established in terms of the Schwarzian derivatives and the second co...

Various linear operators on the class of normalized analytic functions are widely studied. Each satisfies a certain first-order differential recurrence relation. A general class consisting of such operators is introduced. For any operator in this class, a second-order differential subordination implication is investigated on analytic functions gene...

General classes of analytic functions defined by convolution with a fixed analytic function are introduced. Convolution properties of these classes which include the classical classes of starlike, convex, close-to-convex, and quasiconvex analytic functions are investigated. These classes are shown to be closed under convolution with prestarlike fun...