Coefficient estimates for some classes of p -valent functions

M. K. Aouf

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

Let A p , where p is a positive integer, denote the class of functions f ( z ) = z p + ∑ n = p + 1 a n z n which are analytic in U = { z : | z | < 1 } .

For 0 < λ ≤ 1 , | α | < π 2 , 0 ≤ β < p , let F λ ( α , β , p ) denote the class of functions f ( z ) ∈ A p which satisfy the condition | H ( f ( z ) ) − 1 H ( f ( z ) ) + 1 | < λ for z ∈ U , where H ( f ( z ) ) = e i α z f ′ ( z ) f ( z ) − β cos α − i p sin α ( p − β ) cos α .

Also let C λ ( b , p ) , where p is a positive integer, 0 < λ < 1 , and b ≠ 0 is any complex number, denote the class of functions g ( z ) ∈ A p which satisfy the condition | H ( g ( z ) ) − 1 H ( g ( z ) ) + 1 | < λ for z ∈ U , where H ( g ( z ) ) = 1 + 1 p b ( 1 + z g ″ ( z ) g ′ ( z ) − p ) .

In this paper we obtain sharp coefficient estimates for the above mentioned classes.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:136791

DOI: 10.1155/S0161171288000092

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