On certain classes of p -Valent functions

M. K. Aouf

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-10

Abstract:

Let V k λ ( α , b , p ) ( k ≥ 2 , b ≠ 0 is any complex number, 0 ≤ α < p and | λ | < π / 2 ) denote the class of functions f ( z ) = z p + ∑ n = p + 1 ∞ a n z n analytic in U = { z : | z | < 1 } having ( p − 1 ) critical points in U and satisfying lim r → 1 − sup ∫ 0 2 π | Re { e i λ [ p + 1 b ( 1 + z f ″ ( z ) f ′ ( z ) − p ) ] − α cos λ } p − α | d θ ≤ k π cos λ . In this paper we generalize both those functions f ( z ) which are p -valent convex of order α , 0 ≤ α < p , with bounded boundary rotation and those p -valent functions f ( z ) for which z f ′ ( z ) / p is λ -spirallike of order α , 0 ≤ α < p .

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:204023

DOI: 10.1155/S0161171286000078

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