Results & Lemmas (7)
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THEOREM 1.
THEOREM 1. // f(z) e S*(α) and g(z) e S*(τ), then the function F(z) defined by 173
THEOREM 1. // f(z) e S*(α) and g(z) e S*(τ), then the function F(z) defined by 173
Theorem 1
Theorem 1, together with the fact that every convex function is a starlike function of order 1/2, implies the following corollary.…
Theorem 1, together with the fact that every convex function is a starlike function of order 1/2, implies the following corollary. COROLLARY. If f(z)e S*(a) and g(z) is a convex univalent func-
Theorem 1
Theorem 1, we prove two elementary lemmas which are important for our considerations.
Theorem 1, we prove two elementary lemmas which are important for our considerations.
LEMMA 1.
LEMMA 1. Suppose p(z) = [1 + Dw(z)][l + Bwiz)]' 1 where w(z) is regular in E, w(0) = 0, | w(z) | < 1 for zeE and — 1 S D < B ^ 1; then for…
LEMMA 1. Suppose p(z) = [1 + Dw(z)][l + Bwiz)]' 1 where w(z) is regular in E, w(0) = 0, | w(z) | < 1 for zeE and — 1 S D < B ^ 1; then for any C ^ B, we have on \ z \ = r < 1, Re \cp(z L(r) for JR. ^ 2(r) /or Bo^ where c ~ D(B 2 + C)r 4]
THEOREM 2.
THEOREM 2. Let g(z) e S*(Ύ) and F(z) e S*(a) and define f(z) by F z)g z) = 2[f(t)dt, Jo or, equίvalently, by f(z) = 2- ί(g(z)F(z))', then…
THEOREM 2. Let g(z) e S*(Ύ) and F(z) e S*(a) and define f(z) by F{z)g{z) = 2[f(t)dt , Jo or, equίvalently, by f(z) = 2- ί(g(z)F(z))' , then for | z \ = r, β L f{z) J = [P2(r) for R^R,, where
THEOREM 3.
THEOREM 3. If the family Q is defined by
THEOREM 3. If the family Q is defined by
Theorem 2.
Theorem 2.
Theorem 2.
Function classes studied:
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