On alpha-close-to-convex functions of order beta

M. A. Nasr

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-4

Abstract:

Let M β ( α ) [ α ≥ 0 and β ≥ 0 ] denote the class of all functions f ( z ) = z + ∑ n = 2 ∞ a n z n analytic in the unit disc U with f ′ ( z ) f ( z ) / z ≠ 0 and which satisfy for z = r e i θ ∈ U the condition ∫ θ 1 θ 2 Re { ( 1 − α ) z f ′ ( z ) f ( z ) + α ( 1 + z f ″ ( z ) f ′ ( z ) ) } d θ > − β π for all θ 2 > θ 1 . In this note we show that each f ∈ M β ( α ) is close-to-star of order β when 0 < β ≤ α .

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:540937

DOI: 10.1155/S016117128600056X

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