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E-mail: darwish333@yahoo.com Received Nobember 6
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DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE MANSOURA UNIVERSITY MANSOURA
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
Demonstratio Mathematica – de Gruyter
Published: Oct 1, 2008
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