Bemerkungen zu einem Satz von Fejér

Wirths, Karl-Joachim

doi:10.1007/bf02333180

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“…Related problems were considered in [2,12], by imposing an additional condition on f . In Theorem 2.3, we impose conditions on f ∈ A n := {f ∈ A : [2,12] and obtain the starlikeness Univalence and integral transforms…”

Section: Introductionmentioning

confidence: 99%

Univalence, strong starlikeness and integral transforms

Obradović¹,

Ponnusamy

Vasundhra

2005

Ann. Polon. Math.

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Abstract. Let A represent the class of all normalized analytic functions f in the unit disc ∆. In the present work, we first obtain a necessary condition for convex functions in ∆. Conditions are established for a certain combination of functions to be starlike or convex in ∆. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on f and µ so that the non-linear integral transformµ dζ is univalent in ∆. Finally, we give sufficient conditions for functions to be strongly starlike of order α.

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