Results & Lemmas (5)
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Theorem 1.
Theorem 1. c社1,p(A, B) C Cn,p(A, B), n > -p.
Theorem 1. c社1,p(A, B) C Cn,p(A, B), n > -p.
Theorem 3.
Theorem 3. Let p be a positive integer and n is any integer such that n > -p and F(z) = (n + p)z-n 一2p 瓦tn+2p-l f(t)dt. Then FcCn+l,p(A, B)…
Theorem 3. Let p be a positive integer and n is any integer such that n > -p and F(z) = (n + p)z-n 一2p 瓦tn+2p-l f(t)dt. Then FcCn+l,p(A, B) if and only if fcCn,p(A, B).
Theorem 4.
Theorem 4. Let f(z) =令+尹+尹+…. If fcCn,p(A, B), then p(A- B) ·lak-11~,, 、, ，、， k=l,2,..., (17) where a(n,j) = (n + P + j - 1) /· n+p-l. Then…
Theorem 4. Let f(z) =令+尹+尹+…. If fcCn,p(A, B), then p(A- B) ·lak-11~,, 、, ，、， k=l,2, ... , (17) where a(n,j) = (n + P + j - 1) /· n+p-l . Then resu t is sharp.
Theorem 5.
Theorem 5. Let the function f(z) = 士+尹+尹+... be regular in E and --1'.:S B < 0. If 立- p)(1 - B)a(n, k)lak-1 丨~p(A- B) k=l where c,(n, k) =…
Theorem 5. Let the function f(z) = 士+尹+尹+... be regular in E and --1'.:S B < 0. If 立- p)(1 - B)a(n, k)lak-1 丨~p(A- B) k=l where c,(n, k) = (n! ~-~ ~ ~- 1) , then fEC'n ,P(A ,_B). The result is sharp.
Theorem 6.
Theorem 6. If the functions f and g belong to the class Cn,p(A, B) and 0::; s:s; 1, then the function F defind by F(z) = sf(z)+(l-s)g(z)…
Theorem 6. If the functions f and g belong to the class Cn,p(A, B) and 0::; s :s; 1, then the function F defind by F(z) = sf(z)+(l-s)g(z) also belongs to Cn,p(A, B). References (I] M. D. Ganigi and B. A. Uralegaddi, "Subc區ses of meromorphic close-to-convex func tions," Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 33(81) (1989), No. 2 105-109. (2] I. S. Jack, "Functions Starlike and convex of order a," J. London Math. Soc. (2) 3 (1971), 469-474. [3] Vinod Kumar and S. L. Shukla, "Multivalen
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