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ON A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS WITH FIXED SECOND COEFFICIENT

ON A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS WITH FIXED SECOND COEFFICIENT DEMONSTRATIO MATHEMATICAVol. XLINo 42008H. E. DarwishO N A S U B C L A S S OF U N I F O R M L Y C O N V E X F U N C T I O N SWITH FIXED SECOND COEFFICIENTAbstract. Using of Salagean operator, we define a new subclass of uniformly convexfunctions with negative coefficients a n d with fixed second coefficient. T h e main objectiveof this p a p e r is t o obtain coefficient estimates, distortion bounds, closure theorems a n dextreme points for functions belonging of this new class. T h e results are generalized t ofamilies with fixed finitely m a n y coefficients.1. IntroductionLet S denote the class of functions of the form:00(1.1)k=2which are analytic and univalent in the open unit disc U = {z :\z\ <1}, letST and CV the subclasses of S that are, respectively, starlike and convex.Goodman ([8] and [9]) introduced and defined the following subclasses ofCV and ST.A function f(z) is uniformly convex (uniformly starlike) in U if f(z) isin CV(ST) and has the property that for every circular arc 7 contained inU, with center ( also in U, the arcis convex (starlike) with http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS WITH FIXED SECOND COEFFICIENT

Demonstratio Mathematica , Volume 41 (4): 14 – Oct 1, 2008

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References (34)

Publisher
de Gruyter
Copyright
© by H. E. Darwish
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0407
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLINo 42008H. E. DarwishO N A S U B C L A S S OF U N I F O R M L Y C O N V E X F U N C T I O N SWITH FIXED SECOND COEFFICIENTAbstract. Using of Salagean operator, we define a new subclass of uniformly convexfunctions with negative coefficients a n d with fixed second coefficient. T h e main objectiveof this p a p e r is t o obtain coefficient estimates, distortion bounds, closure theorems a n dextreme points for functions belonging of this new class. T h e results are generalized t ofamilies with fixed finitely m a n y coefficients.1. IntroductionLet S denote the class of functions of the form:00(1.1)k=2which are analytic and univalent in the open unit disc U = {z :\z\ <1}, letST and CV the subclasses of S that are, respectively, starlike and convex.Goodman ([8] and [9]) introduced and defined the following subclasses ofCV and ST.A function f(z) is uniformly convex (uniformly starlike) in U if f(z) isin CV(ST) and has the property that for every circular arc 7 contained inU, with center ( also in U, the arcis convex (starlike) with

Journal

Demonstratio Mathematicade Gruyter

Published: Oct 1, 2008

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