Some properties concerning close-to-convexity of certain analytic functions

Abstract

Let f (z) be an analytic function in the open unit disk D normalized with f (0) = 0 and f (0) = 1. With the help of subordinations, for convex functions f (z) in D, the order of close-to-convexity for f (z) is discussed with some example. MSC: Primary 30C45

On the Starlikeness for Certain Analytic Functions

“…Lemma 2.2. (see [6])Let     be a positive real number. Then suppose that there exists a point 0 zU  such…”

Some conditions on starlike and close to convex functions

“…According to the definitions for the class starlike functions S*(α) and complex functions K(α) which these functions are of α degree. We know that ( ) ( ) ( ) * ( ) zf z S    [1][2][3][4][5]. For the starlike function () fzwith a degree (0 1),   we can give the following function as an example:…”

SOME PROPERTIES OF CERTAIN SUBCLASS OF GENERALIZED p-VALENT LOGARITHMIC λ-BAZILEVIC FUNCTIONS Vol. 4(1) Jan. 2016, No. 4, pp. 25-41 SHU-HAI LI, LI-NA MA, HUO TANG

“…Obviously, for p = 1, λ = 0, A = 1 − 2ρ (0 ≤ ρ < 1) and B = −1 in Definition 1, we have the well-known classes J(α, ρ) (see [14] and [16]; also see [26]). When p = 1, A = 1 and B = −1, if we set λ = 0 and λ = 1 in Definition 1, respectively, we have the well-known classes S * and K. Also, for λ = 0 and p = 1, we obtain the class J 1 [0, A, B] of Janowski starlike functions (see [9], [33], [34]).…”