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...

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Veröffentlicht in:TWMS journal of applied and engineering mathematics Jg. 11; H. 1; S. 250
1. Verfasser: Al-Refai, Oqlah
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Istanbul Turkic World Mathematical Society 01.01.2021
Elman Hasanoglu
Schlagworte:
Engineering research
Functional equations
Functions
Functions of complex variables
Inequalities (Mathematics)
Mathematical research
Meromorphic functions
Saudi Arabia
ISSN:2146-1147, 2146-1147
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Zusammenfassung: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
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ISSN:2146-1147
2146-1147