On some differential subordination theorems of multivalent functions involving integral operator

Some Subordination Results of Multivalent Functions Defined by Integral Operator

Properties of multivalent functions associated with certain integral operator

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

Convolution and Differential Subordination for Multivalent Functions

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

Generalized Integral Operator and Multivalent Functions

Let A(p) be the class of functions f : f(z) = z + ∑∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1(z) = z p (1−z)n+p . We define f (−1) n+p−1(z) by using convolution ? as fn+p−1(z) ? f (−1) n+p−1(z) = z (1−z)n+p . A function p, analytic in E with p(0) = 1, is in the class Pk(ρ) if ∫ 2π 0 ∣∣∣Rep(z)−ρ p−ρ ∣∣∣ dθ ≤ kπ, where z = re, k ≥ 2 and 0 ≤ ρ < p. We use t...

properties of multivalent functions associated with certain integral operator

let a(p) denote the class of functions which are analytic in the open unit disk u. by making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.