M. K AOUF

On p - valent functions with negative and missing coefficients

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

Let Pfc (p, A, B, a) be the class of functions f (z) — :p7A |a p - |zP+n’k - 2, analytic and p-valent in the unit disc U = |z: | z j < 1 | and satisfying the condition 1, z e U, zf,(zL - p 'f ( z ) [pB + (A -B ) (P -a )l - B zf'(z) f(z) where - 1 < B < A < 1, -1 < B < 0 , and 0 < a < p. In this paper we obtain coefficient estimate, distortion and closure theorems and the radius of convexity for the class Pk (p, A, B, a). We also obtain class preserving integral ope- rators of the form F(z) f t ^ 1 f(t) dt, e > - p Zç O for the class Pk (p, A, B, a). Conversely when F (z) £ Pk (p, A, B, a), radius of p-valence of f (z) has been determined.

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