On a subclass of α -convex λ -spiral functions

F. M. Al-Oboudi and M. M. Hidan

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 30, 1-7

Abstract:

Let H denote the class of functions f ( z ) = z + ∑ k = 2 ∞ a k z k which are analytic in the unit disc Δ = { z : | z | < 1 } . In this paper, we introduce the class M α λ [ A , B ] of functions f ∈ H with f ( z ) f ′ ( z ) / z ≠ 0 , satisfying for z ∈ Δ : { ( e i λ − α cos λ ) ( z f ′ ( z ) / f ( z ) ) + α cos λ ( 1 + z f ″ ( z ) / f ′ ( z ) ) } ≺ cos λ ( ( 1 + A z ) / ( 1 + B z ) ) + i sin λ , where ≺ denotes subordination, α and λ are real numbers, | λ | < π / 2 and − 1 ≤ B < A ≤ 1 . Functions in M α λ [ A , B ] are shown to be λ -spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:943130

DOI: 10.1155/S0161171202011110

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