Neighborhoods of Starlike and Convex Functions Associated with Parabola

Neighborhoods of Starlike and Convex Functions Associated with Parabola

Let f be a normalized analytic function defined on the unit disk and fλ z : 1 − λ z λf z for 0 < λ ≤ 1. For α > 0, a function f ∈ SP α, λ if zf ′ z /fλ z lies in the parabolic region Ω : {w : |w − α| < Rew α}. Let CP α, λ be the corresponding class consisting of functions f such that zf ′ z ′/f ′ λ z lies in the region Ω. For an appropriate δ > 0, the δ-neighbourhood of a function f ∈ CP α, λ i...

Convex and Starlike Univalent Functions

Classes of uniformly starlike and convex functions

Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated. 1. Introduction. Let A denote the class of functions of the form f (z) = z+ ∞ n=2 a n z

Parabolic Starlike and Uniformly Convex Functions

The main object of this paper is to derive the sufficient conditions for the function z {pψq (z)} to be in the class of uniformly starlike and uniformly convex function associated with the parabolic region Re {ω} > |ω − 1| . Further, the hadamard product of the function which are analytic in the open unit disk with negative coefficients are also investigated. Finally, similar results using an i...

Integral Means for Uniformly Convex and Starlike Functions Associated with Generalized Hypergeometric Functions

Making use of the generalized hypergeometric functions, we introduce some generalized class of k−uniformly convex and starlike functions and for this class, we settle the Silverman’s conjecture for the integral means inequality. In particular, we obtain integral means inequalities for various classes of uniformly convex and uniformly starlike functions in the unit disc.