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ON k-SYMMETRIC QUASI-STARLIKE MEROMORPHIC FUNCTIONS

ON k-SYMMETRIC QUASI-STARLIKE MEROMORPHIC FUNCTIONS DEMONSTRATIO MATHEMATICAVol. IVNo 41973Krystyna DobrowolskaO N k-SYMMETRIC QUASI-STARLIKE M E R O M O R P H I C FUNCTIONS1. Introduction. In the earlier paper [l] we introduced theclassof functions f meromorphic in the disc|z-|<1 (withpole at z=0) defined by the equation= MF(z),whereM|z|< 1,(1)is an arbitrary fixed number in the interval (1, » )*F- an arbitrary function of the class >_ , i.e. a1)like meromorphic function .andThe functions of the classromorphicstar-were called quasi-starlike me-functions.In the present work we shall consider, for anfixed natural number k, the classf^=£ank-1n-0zIlkJ^^^c~1'aarbitraryfunctions-1 =M'satisfying the conditione(f ^z e¥i\J =The functions of the classquasi-starlike meromorphicf(z).^gcalledk-symmetricfunctions.^ F(z) maps the disc |z|<1 onto a domain where complement is starlike with respect to the origin.- 251 -K.Dobrowolska2I t can be shown that f ei f and only i f the function P appearing in (1) belongs to the class L * ^ ^ i . e . i t i sa k-symmetric starlike meromorphic function with the expansionof the formtoo= Lr>"0Ank-1zDk_1,A-1 =<30Moreover, i t can be shown that f ef e L ^, whereLetf(z) =i f and only i fVf(zk).denote the class of functions of the form (2)defined by equation (1) in whichF(z) 4n(i-«tz k)t.where<at = e 9 ^,-real,<5^ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON k-SYMMETRIC QUASI-STARLIKE MEROMORPHIC FUNCTIONS

Dobrowolska, Krystyna
Demonstratio Mathematica , Volume 4 (4): 22 – Oct 1, 1972
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Publisher
de Gruyter
Copyright
© by Krystyna Dobrowolska
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1972-0407
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. IVNo 41973Krystyna DobrowolskaO N k-SYMMETRIC QUASI-STARLIKE M E R O M O R P H I C FUNCTIONS1. Introduction. In the earlier paper [l] we introduced theclassof functions f meromorphic in the disc|z-|<1 (withpole at z=0) defined by the equation= MF(z),whereM|z|< 1,(1)is an arbitrary fixed number in the interval (1, » )*F- an arbitrary function of the class >_ , i.e. a1)like meromorphic function .andThe functions of the classromorphicstar-were called quasi-starlike me-functions.In the present work we shall consider, for anfixed natural number k, the classf^=£ank-1n-0zIlkJ^^^c~1'aarbitraryfunctions-1 =M'satisfying the conditione(f ^z e¥i\J =The functions of the classquasi-starlike meromorphicf(z).^gcalledk-symmetricfunctions.^ F(z) maps the disc |z|<1 onto a domain where complement is starlike with respect to the origin.- 251 -K.Dobrowolska2I t can be shown that f ei f and only i f the function P appearing in (1) belongs to the class L * ^ ^ i . e . i t i sa k-symmetric starlike meromorphic function with the expansionof the formtoo= Lr>"0Ank-1zDk_1,A-1 =<30Moreover, i t can be shown that f ef e L ^, whereLetf(z) =i f and only i fVf(zk).denote the class of functions of the form (2)defined by equation (1) in whichF(z) 4n(i-«tz k)t.where<at = e 9 ^,-real,<5^

Journal

Demonstratio Mathematica – de Gruyter

Published: Oct 1, 1972

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