Some classes of alpha-quasi-convex functions

Khalida Inayat Noor

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-5

Abstract:

Let C [ C , D ] , − 1 ≤ D < C ≤ 1 denote the class of functions g , g ( 0 ) = 0 , g ′ ( 0 ) = 1 , analytic in the unit disk E such that ( z g ′ ( z ) ) ′ g ′ ( z ) is subordinate to 1 + C Z 1 + D Z , z ∈ E . We investigate some classes of Alpha-Quasi-Convex Functions f , with f ( 0 ) = f ′ ( 0 ) − 1 = 0 for which there exists a g ∈ C [ C , D ] such that ( 1 − α ) f ′ ( z ) g ′ ( z ) + α ( z f ′ ( z ) ) ′ g ′ ( z ) is subordinate to 1 + A Z 1 + B Z ′ , − 1 ≤ B < A ≤ 1 . Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:275245

DOI: 10.1155/S0161171288000584

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