On p - valent functions with negative and missing coefficients

Authors : M K AOUF

Pages : 0-0

Doi:10.1501/Commua1_0000000452

View : 16 | Download : 8

Publication Date : 1995-01-01

Article Type : Research Paper

Abstract :Let Pfc insert ignore into journalissuearticles values(p, A, B, a); be the class of functions f insert ignore into journalissuearticles values(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, zfinsert ignore into journalissuearticles values(zL - p `f insert ignore into journalissuearticles values( z ); [pB + insert ignore into journalissuearticles values(A -B ); insert ignore into journalissuearticles values(P -a );l - B zf`insert ignore into journalissuearticles values(z); finsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(p, A, B, a);. We also obtain class preserving integral ope- rators of the form Finsert ignore into journalissuearticles values(z); f t ^ 1 finsert ignore into journalissuearticles values(t); dt, e > - p Zç O for the class Pk insert ignore into journalissuearticles values(p, A, B, a);. Conversely when F insert ignore into journalissuearticles values(z); £ Pk insert ignore into journalissuearticles values(p, A, B, a);, radius of p-valence of f insert ignore into journalissuearticles values(z); has been determined.
Keywords : p valent, coefficients, missing