On a Class of p-valent Functions with Negative and Missing Coefficients

다국어 초록 (Multilingual Abstract)

Let T^(*)_(p,t) (A,B,α)be the class of functionse f(x) = z^(p)-∑^(∞)_(n=k+1) a_(n)zⁿ, a_(n)≥0, k≥p≥1, analytic and p-valent in the unit disc and satisfying
◁수식 삽입▷ (원문을 참조하세요)
for z in the unit disc and where -1 ≤ B < A ≤ 1, 0 ≤ α <p, f_(t)(z)= (1-t)z^(p) +tf(z), 0≤t≤1.
In this paper, we obtain coefficient, estimate, distortion and closure theorems, radius of conversity estimates, convolution properties et cetera, for the class T^(*)_(p,t) (A,B,α) under the assumption that -1 ≤ B ＜ 0. We also obtain the calss preserving integral operatos of the form
◁수식 삽입▷ (원문을 참조하세요)
for the class T^(*)_(p,t) (A,B,α)