SHARP INEQUALITIES FOR UNIVALENCE OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED UNIT DISK

A new class of meromorphic functions f that are univalent in the punctured unit disk U* = z : 0 < |z| < 1 is introduced. This class is denoted by MU and consisting of functions f defined by |1 + f' (z)/f (2)(z)| < 1 and zf (z) [not equal to] 0, whenever z [member of] U = z : |z| < 1...

Full description

Saved in:
Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics Vol. 11; no. 1; p. 250
Main Author: Al-Refai, Oqlah
Format: Journal Article
Language:English
Published: Istanbul Turkic World Mathematical Society 01.01.2021
Elman Hasanoglu
Subjects:
Engineering research
Functional equations
Functions
Functions of complex variables
Inequalities (Mathematics)
Mathematical research
Meromorphic functions
Saudi Arabia
ISSN:2146-1147, 2146-1147
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A new class of meromorphic functions f that are univalent in the punctured unit disk U* = z : 0 < |z| < 1 is introduced. This class is denoted by MU and consisting of functions f defined by |1 + f' (z)/f (2)(z)| < 1 and zf (z) [not equal to] 0, whenever z [member of] U = z : |z| < 1. For every n [greater than or equal to] 2, sharp bound for the nth derivative of 1/(zf (z)) that implies univalency of f in U (*) is established. In particular, the best improvements for known univalence criteria are obtained. Distortion and growth estimates are investigated. Further, various sufficient coefficient conditions and a necessary coefficient condition for f to be in MU are derived and best radii of univalence are obtained for certain cases. Keywords: univalent functions, meromorphic functions, distortion theorem, coefficient bounds, area theorem. AMS Subject Classification: 30C45, 30C55
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2146-1147
2146-1147