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Suppose that n is a positive integer. For any real number α(β resp.) with α < 1 (β > 1 resp.), let Khni(α) (Khni(β) resp.) be the class of analytic functions in the unit disk D with f(0) = f0(0) = · · · =f(n−1)(0) = f(n)(0)−1 = 0, Re[수식]>α[수식]< β resp.) in D, and for any ¸ ε D, let Khni(α,λ ¸) (Khni(β,λ¸) resp.) denote a subclass of Khni(α) (Khni(β) resp.) whose elements satisfy some condition about derivatives. For any fixed z0 ∈ D, we shall determine the two regions of variability V hni(z0, α) (V hni(z0, β) resp.) and V hni(z0, α,λ ¸)(V hni(z0, β,λ ¸) resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy f(D) ⊂ V hni(z0, α) (f(D) ⊂V hni(z0, β) resp.) when f ranges over the classes Khni(α) (Khni(¯) resp.)and Khni(α, λ¸) (Khni(β,λ ¸) resp.), respectively.
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참고문헌 (14)
참고문헌 신청
A. W. Goodman / 1983 / Univalent Functions, Vols. I and II / Mariner Publishing Co.
Ch. Pommerenke / 1992 / Boundary Behaviour of Conform Maps / Springer-Verlag
D. J. Hallenbeck / 1974 / Extreme points of classes of functions defined by subordination / Proc. Amer. Math. Soc. : 59 ~ 64
D. J. Hallenbeck / 1976 / Applications of extreme point theory to classes of multivalent functions / Trans. Amer. Math. Soc. 221 (2) : 339 ~ 359
H. Yanagihara / 2005 / Regions of variability for functions of bounded derivatives / Kodai Math. J. 28 (2) : 452 ~ 462
Ch. Pommerenke / 1992 / Boundary Behaviour of Conform Maps / Springer-Verlag
D. J. Hallenbeck / 1974 / Extreme points of classes of functions defined by subordination / Proc. Amer. Math. Soc. : 59 ~ 64
D. J. Hallenbeck / 1976 / Applications of extreme point theory to classes of multivalent functions / Trans. Amer. Math. Soc. 221 (2) : 339 ~ 359
H. Yanagihara / 2005 / Regions of variability for functions of bounded derivatives / Kodai Math. J. 28 (2) : 452 ~ 462
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