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FIXED COEFFICIENTS FOR NEW CLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

FIXED COEFFICIENTS FOR NEW CLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS D E M O N S T R A T E MATHEMATICAVol. X X XNo 11997M. K. Aouf, H. E. DarwishFIXED COEFFICIENTS FOR NEW CLASSESOF UNIVALENT FUNCTIONSWITH NEGATIVE COEFFICIENTSIn this paper we consider the classc consisting of analytic and univalent functions with negative coefficients and fixed second coefficient. Theobject of the present paper is to show coefficient estimates, convex linearpaper is to show coefficient estimates, convex linear combination, some distortion theorems and radii of starlikeness and convexity for f(z) in the classR*n c . The results are generalized to families with finitely many fixed coefficients.1. IntroductionLet A stands for the class of functions of the formoo(1.1)which are analytic in the unit disc U = {z :We denote by S thesubclass of univalent functions f(z) in A. The Hadamard product of twofunctions f ( z ) £ A and g(z) 6 A will be denoted by f * g ( z ) , that is, if f ( z )is given by (1.1) and g(z) is given byoo(1.2)k=2thenoo(1.3)1991 MathematicsSubject Classification:Key words and phrases:30C45.univalent, Ruscheweyh derivative, extreme points.M. K. A o u f , H. E. D a r w i s h44Letz[2 B " 1 /(*)] ( n )nlDnf(z)(1.4)for n http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

FIXED COEFFICIENTS FOR NEW CLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

Aouf, M. K.; Darwish, H. E.
Demonstratio Mathematica , Volume 30 (1): 10 – Jan 1, 1997
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References (4)

Publisher
de Gruyter
Copyright
© by M. K. Aouf
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1997-0106
Publisher site
See Article on Publisher Site

Abstract

D E M O N S T R A T E MATHEMATICAVol. X X XNo 11997M. K. Aouf, H. E. DarwishFIXED COEFFICIENTS FOR NEW CLASSESOF UNIVALENT FUNCTIONSWITH NEGATIVE COEFFICIENTSIn this paper we consider the classc consisting of analytic and univalent functions with negative coefficients and fixed second coefficient. Theobject of the present paper is to show coefficient estimates, convex linearpaper is to show coefficient estimates, convex linear combination, some distortion theorems and radii of starlikeness and convexity for f(z) in the classR*n c . The results are generalized to families with finitely many fixed coefficients.1. IntroductionLet A stands for the class of functions of the formoo(1.1)which are analytic in the unit disc U = {z :We denote by S thesubclass of univalent functions f(z) in A. The Hadamard product of twofunctions f ( z ) £ A and g(z) 6 A will be denoted by f * g ( z ) , that is, if f ( z )is given by (1.1) and g(z) is given byoo(1.2)k=2thenoo(1.3)1991 MathematicsSubject Classification:Key words and phrases:30C45.univalent, Ruscheweyh derivative, extreme points.M. K. A o u f , H. E. D a r w i s h44Letz[2 B " 1 /(*)] ( n )nlDnf(z)(1.4)for n

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 1997

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