Abstract
Let S denote the class of functions that are analytic, normalized and univalent
in the open unit disk
{
}
:
1
E
z
z
=
<
. Subclasses of S are the class of starlike
and convex functions denoted by
*
S and C respectively. A new subclass of
analytic functions that generalize some known subclasses of analytic func-
tions was defined and investigated. We obtained coefficient bounds, upper
estimates for the Fekete-Szegö functional and the Hankel determinant.
Results & Lemmas (6)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Lemma 2.1.
Lemma 2.1. Let p P ∈. Then ( ) 2 kc k ≤ ∈ [12] (2.1)
Lemma 2.1. Let p P ∈ . Then ( ) 2 kc k ≤ ∈ [12] (2.1)
Lemma 2.2.
Lemma 2.2. Let p P ∈, then for any real λ ( ) ( ) 2 1 2 2 1 if 0 2
Lemma 2.2. Let p P ∈ , then for any real λ ( ) ( ) 2 1 2 2 1 if 0 2
Lemma 2.3.
Lemma 2.3. Let p P ∈ then ( ) 2 2 2 1 1 2 4 c c
Lemma 2.3. Let p P ∈ then ( ) 2 2 2 1 1 2 4 c c
Theorem 3.1.
Theorem 3.1. Let ( ) ( ) [ ],, 0,1,, 2 2 n f z C
Theorem 3.1. Let ( ) ( ) [ ] , , 0,1 , , 2 2 n f z C
Theorem 3.2.
Theorem 3.2. Let ( ) ( ), n f z C β γ ∈, then for any real number µ 2 2 1 2
Theorem 3.2. Let ( ) ( ) , n f z C β γ ∈ , then for any real number µ 2 2 1 2
Theorem 3.3
Theorem 3.3 Let ( ) ( ) [ ],, 0,1,, 2 2 n f z C
Theorem 3.3 Let ( ) ( ) [ ] , , 0,1 , , 2 2 n f z C
Definitions (1)
Def 1.1.
Definition 1.1. A function ( ) f z of the form (1.1) analytic and univalent in U is said to be in the ( ) [ ],
Definition 1.1. A function ( ) f z of the form (1.1) analytic and univalent in U is said to be in the ( ) [ ] ,