Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Radius of β-Convexity for Certain Family of Functions Meromorphic in the Unit Disc

On the Radius of β-Convexity for Certain Family of Functions Meromorphic in the Unit Disc DEMONSTRATIO MATHEMATICAVoLVmNo «1975Ryszard MazurON THE RADIUS OF /?-CONVEXITY FOR CERTAIN FAMILYOF FUNCTIONS MEROMORPfflC IN THE UNIT DISCLet O denote a family of functions w holomorphic in theunit d i s c K =: | z | < l | and normed "by the conditions w(0) == 0 , | to (Z) | < 1 f o r z e K. Let V (A) denote the c l a s s offunctions P(z) defined "by the formula(1.1)P(z)= 1 + ACJ(Z),zeK,where weft and A i s a f i x e d number i n the i n t e r v a l ( 0 , 1 } .I t i s easy to see that ^(A)c V where V i s the c l a s soffunctions p(z) = 1 + p^z + p 2 z +re p ( z ) > 0 f o r z € K.I t i s known ( [ l ] , [ 2 ] ) that P e f ( k ) i f and only i f(1.2)wherePCs),=pe?Let f ^ k } denote a s u b c l a s s of the family ^(A) consisting of those functions P of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

On the Radius of β-Convexity for Certain Family of Functions Meromorphic in the Unit Disc

Mazur, Ryszard
Demonstratio Mathematica , Volume 8 (4): 8 – Oct 1, 1975
Download PDF
8 pages

Loading next page...
 
/lp/de-gruyter/on-the-radius-of-convexity-for-certain-family-of-functions-meromorphic-hqCg6k1Z3c

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© by Ryszard Mazur
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1975-0409
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVoLVmNo «1975Ryszard MazurON THE RADIUS OF /?-CONVEXITY FOR CERTAIN FAMILYOF FUNCTIONS MEROMORPfflC IN THE UNIT DISCLet O denote a family of functions w holomorphic in theunit d i s c K =: | z | < l | and normed "by the conditions w(0) == 0 , | to (Z) | < 1 f o r z e K. Let V (A) denote the c l a s s offunctions P(z) defined "by the formula(1.1)P(z)= 1 + ACJ(Z),zeK,where weft and A i s a f i x e d number i n the i n t e r v a l ( 0 , 1 } .I t i s easy to see that ^(A)c V where V i s the c l a s soffunctions p(z) = 1 + p^z + p 2 z +re p ( z ) > 0 f o r z € K.I t i s known ( [ l ] , [ 2 ] ) that P e f ( k ) i f and only i f(1.2)wherePCs),=pe?Let f ^ k } denote a s u b c l a s s of the family ^(A) consisting of those functions P of

Journal

Demonstratio Mathematica – de Gruyter

Published: Oct 1, 1975

There are no references for this article.