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Bounded functions starlike with respect to symmetrical points

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  • Fatima M. Al-Oboudi

Abstract

Let P [ A , B ] , − 1 ≤ B < A ≤ 1 , be the class of functions p analytic in the unit disk E with p ( 0 ) = 1 and subordinate to 1 + A z 1 + B z . In this paper we define and study the classes S S * [ A , B ] of functions starlike with respect to symmetrical points. A function f analytic in E and given by f ( z ) = z + ∑ n = 2 ∞ a n z n is said to be in S S * [ A , B ] if and only if, for z ∈ E , 2 z f ′ ( z ) f ( z ) − f ( − z ) ∈ P [ A , B ] . Basic results on S S * [ A , B ] are studied such as coefficient bounds, distortion and rotation theorems, the analogue of the Polya-Schoenberg conjecture and others.

Suggested Citation

  • Fatima M. Al-Oboudi, 1996. "Bounded functions starlike with respect to symmetrical points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:534046
    DOI: 10.1155/S0161171296000877
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