🧭 New here?
Take a guided tour of the site.
← Back to Papers

The Fekete Szegö Functional and Second Hankel Determinant for a Certain Sublass of Analytic Functions

Rasheed O. Ayinla, Timothy O. Opoola · 2019 📄 DOI →

Continue from this paper

Indexing is not verification. Extracted statements should be checked against the source.

Read the original paper ↗ Search this title Learn what Atlas can verify → Suggest a correction or ask a question →
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 ( ) [ ] ,
↑↓ navigate↵ openesc closeall results
✦ 291 explorers have wandered the registry - thanks for stopping by. Tell us what you'd like to see →
Usage & privacy

We use first-party site metrics to improve navigation: page visits, internal clicks, search result counts (not search terms), and approximate active time. A random tab ID groups events for seven days; GPC/DNT turns this off. The separate visitor count uses a self-hosted pseudonymous fingerprint and also respects GPC/DNT.

💬 Feedback