Abstract
In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.
Highlights
Let p ∈ N = {1, 2, . . .} and denote Ap as the class of multivalent functions of the form ∞f (z) = zp + ∑ anzn, (1)n=p+1 which are analytic in the open unit disk:U = {z ∈ C : |z| < 1} . (2)For two parameters α ∈ [−p, p] and β ≥ 0, function f(z) ∈ Ap is said to be in class UST(p, α, β) of p-valent β-uniformly star-like functions of order α in U, if and only ifR ( zf (z) f (z) − α)
N=p+1 which are analytic in the open unit disk: U = {z ∈ C : |z| < 1}
We derive sufficient conditions for f(z) which are given by using coefficient inequalities
Summary
Srivastava et al in [6] introduced a subclass of the p-valent function class USm(p, q; α, β) consisting of functions f(z) of form (1), which satisfy the following analytic criterion: for all z ∈ U, zmf(q+m) (z) f(q) (z). A. Noor in [9] defined some subclasses of analytic functions related to k-uniformly close-to-convex functions of higher order and studied the following: rate of growth of coefficients, inclusion relations, radius problems, and necessary conditions for univalency. Following Srivastava et al [6] and Nishiwaki and Owa [5], we define a new subclass MDm(p, q; α, β) of multivalent functions involving higher-order derivative. We obtain several properties including the coefficient inequalities, distortion theorems, extreme points, and integral means inequalities for this subclass MDm(p, q; α, β) of multivalent functions involving higher-order derivative
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
