Univalence and Starlikeness of Certain Classes of Analytic Functions

Najla M. Alarifi; M. Obradović

doi:10.3390/sym15051014

Univalence and Starlikeness of Certain Classes of Analytic Functions

Najla M. Alarifi^*
, M. Obradović

^*Corresponding author for this work

Mathematics Department

Faculty of Civil Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For the analytic functions (Formula presented.) in the unit disk (Formula presented.) we calculate the values of n and (Formula presented.) where the condition (Formula presented.) or (Formula presented.) (Formula presented.) yields univalence and starlikeness. Conditions imply (Formula presented.) in the class where all normalized analytic functions (Formula presented.) with (Formula presented.) (Formula presented.) are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.

Original language	English
Article number	1014
Journal	Symmetry
Volume	15
Issue number	5
DOIs	https://doi.org/10.3390/sym15051014
State	Published - May 2023

Keywords

analytic function
convex function
Jack lemma
open unit disk
starlike function
starlike function
subordination
univalent function

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10.3390/sym15051014

Cite this

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title = "Univalence and Starlikeness of Certain Classes of Analytic Functions",

abstract = "For the analytic functions (Formula presented.) in the unit disk (Formula presented.) we calculate the values of n and (Formula presented.) where the condition (Formula presented.) or (Formula presented.) (Formula presented.) yields univalence and starlikeness. Conditions imply (Formula presented.) in the class where all normalized analytic functions (Formula presented.) with (Formula presented.) (Formula presented.) are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.",

keywords = "analytic function, convex function, Jack lemma, open unit disk, starlike function, starlike function, subordination, univalent function",

author = "Alarifi, \{Najla M.\} and M. Obradovi{\'c}",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

year = "2023",

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doi = "10.3390/sym15051014",

language = "English",

volume = "15",

journal = "Symmetry",

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AU - Alarifi, Najla M.

AU - Obradović, M.

PY - 2023/5

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N2 - For the analytic functions (Formula presented.) in the unit disk (Formula presented.) we calculate the values of n and (Formula presented.) where the condition (Formula presented.) or (Formula presented.) (Formula presented.) yields univalence and starlikeness. Conditions imply (Formula presented.) in the class where all normalized analytic functions (Formula presented.) with (Formula presented.) (Formula presented.) are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.

AB - For the analytic functions (Formula presented.) in the unit disk (Formula presented.) we calculate the values of n and (Formula presented.) where the condition (Formula presented.) or (Formula presented.) (Formula presented.) yields univalence and starlikeness. Conditions imply (Formula presented.) in the class where all normalized analytic functions (Formula presented.) with (Formula presented.) (Formula presented.) are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.

KW - analytic function

KW - convex function

KW - Jack lemma

KW - open unit disk

KW - starlike function

KW - subordination

KW - univalent function

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DO - 10.3390/sym15051014

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AN - SCOPUS:85160540021

SN - 2073-8994

VL - 15

JO - Symmetry

JF - Symmetry

IS - 5

M1 - 1014

ER -

Univalence and Starlikeness of Certain Classes of Analytic Functions

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Study Results from Imam Abdulrahman Bin Faisal University Provide New Insights into Mathematics (Univalence and Starlikeness of Certain Classes of Analytic Functions)

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Univalence and Starlikeness of Certain Classes of Analytic Functions

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Study Results from Imam Abdulrahman Bin Faisal University Provide New Insights into Mathematics (Univalence and Starlikeness of Certain Classes of Analytic Functions)

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