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

Learn More →

NEW CRITERIA FOR UNIVALENCE OF CERTAIN INTEGRAL OPERATORS

NEW CRITERIA FOR UNIVALENCE OF CERTAIN INTEGRAL OPERATORS DEMONSTRATIO MATHEMATICAVol. XXXIIINo 12000Virgil PescarN E W CRITERIA FOR UNIVALENCEOF CERTAIN INTEGRAL OPERATORSAbstract. In this work there is considered the class of univalent functions defined bythe condition I 'AS"? — l | < 1, |z| < 1, where f(z) = z + a.2z2 + . . . is analytic in the unitI / (z)Idisc U = {z : \z\ < 1}. The author determines conditions for the univalence of certainintegral operators.1. IntroductionWe denote by S the class of regular and univalent functions f(z) =z + a^z2 + . . . in the unit disc U. Let A be the class of functions f which areanalytic in the unit disc U with /(0) = /'(0) — 1 = 0.In their paper [2] Ozaki and Nunokawa proved the followingTHEOREMA. Assume that f € A satisfies the conditionz2f'{z)(1)- 1f2(z)< l,zeu,then f is univalent in U.2. Preliminary resultsWe shall use the following results.THEOREMB [3]. Let a be a complex number, Rea > 0 and f € A. If(2)1 -|2|2*eaReafor all z €U, then the functionzf"(z)< 1z(3)is in the class S.Fa(z)=[a\ua~1f'(u)du52V. PescarTHEOREM C [4]. Let a be a complex number, Rea > 0 and f(z) = z +CI2Z2 + ... is a regular function http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

NEW CRITERIA FOR UNIVALENCE OF CERTAIN INTEGRAL OPERATORS

Pescar, Virgil
Demonstratio Mathematica , Volume 33 (1): 4 – Jan 1, 2000
Download PDF
4 pages

Loading next page...
 
/lp/de-gruyter/new-criteria-for-univalence-of-certain-integral-operators-I3HOKYUOYP

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 Virgil Pescar
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2000-0107
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIIINo 12000Virgil PescarN E W CRITERIA FOR UNIVALENCEOF CERTAIN INTEGRAL OPERATORSAbstract. In this work there is considered the class of univalent functions defined bythe condition I 'AS"? — l | < 1, |z| < 1, where f(z) = z + a.2z2 + . . . is analytic in the unitI / (z)Idisc U = {z : \z\ < 1}. The author determines conditions for the univalence of certainintegral operators.1. IntroductionWe denote by S the class of regular and univalent functions f(z) =z + a^z2 + . . . in the unit disc U. Let A be the class of functions f which areanalytic in the unit disc U with /(0) = /'(0) — 1 = 0.In their paper [2] Ozaki and Nunokawa proved the followingTHEOREMA. Assume that f € A satisfies the conditionz2f'{z)(1)- 1f2(z)< l,zeu,then f is univalent in U.2. Preliminary resultsWe shall use the following results.THEOREMB [3]. Let a be a complex number, Rea > 0 and f € A. If(2)1 -|2|2*eaReafor all z €U, then the functionzf"(z)< 1z(3)is in the class S.Fa(z)=[a\ua~1f'(u)du52V. PescarTHEOREM C [4]. Let a be a complex number, Rea > 0 and f(z) = z +CI2Z2 + ... is a regular function

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2000

There are no references for this article.