Applications of convolution and‎ ‎subordination to certain $p$-valent functions

Applications of differential subordination to certain subclasses of p-valent meromorphic functions involving a certain operator

By making use of the method of differential subordination, we investigate some properties of certain classes of p-valent meromorphic functions, which are defined by means of a certain operator .

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 $|w^{2}-1|=1$ ...

On Certain Classes of p-Valent Functions by Using Complex-Order and Differential Subordination

The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z Ip r, λ f z j 1 / p − j Ip r, λ f z j ≺ a aB A − B β z /a 1 Bz , where Ip r, λ is an operator defined by Sălăgean and β is a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting pr...

Subordination and Super Ordination Results Involving Certain Convolution Operators

DIFFERENTIAL SUBORDINATION AND SUPERORDINATION RESULTS FOR p-VALENT ANALYTIC FUNCTIONS

Using the fractional integral operator D−λ z and generalized SrivastavaAttiya operator J s,b , we introduce and study some differential subordination and superordination results for p-valent analytic functions in the open unit disk. These results are obtained by investigating appropriate classes of admissible functions.

CONVOLUTION CONDITIONS FOR SPIRALLIKENESS AND CONVEX SPIRALLIKENESS OF CERTAIN MEROMORPHIC p-VALENT FUNCTIONS

In the present investigation, the authors derive necessary and sufficient conditions for spirallikeness and convex spirallikeness of a suitably normalized meromorphic p-valent function in the punctured unit disk, using convolution. Also we give an application of our result to obtain a convolution condition for a class of meromorphic functions defined by a linear operator.