Subordination of polynomials

1 Subordination at the Interface : the Quasi - Subordination Hypothesis

The subordination of clauses, and the recursion which results, lies at the heart of linguistic representation. Yet there are many aspects of subordination that are not fully understood. An enduring puzzle is that some clauses which appear to be structurally subordinate nevertheless pattern with main clauses in certain, but not all, respects. This paper posits that such clauses, which we term “q...

Subordination by convex functions

Fuzzy Differential Subordination

The method of differential subordination or ”admissible functions method” was introduced by P.T. Mocanu and S.S. Miller in [1], [2] and then developed in monography [3], as well as in other papers of other mathematicians. Until now, the notion of differential subordination appears in papers published in various journals specialized in complex analysis around the world. We extend this method to ...

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

Some applications of differential subordination

A number of interesting criteria were given by earlier workers for a normalized analytic function to be in the familiar class ∗ of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator c(c >−1) is also considered.