Journal of the Ramanujan Mathematical Society

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Some Criteria for Univalence in the Unit Disc


Affiliations
1 Department of Mathematics, University of Belgrade, 4 Karnegieva Street, 11000 Belgrade, Yugoslavia, Serbia
     

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The classes Mn, n = 0, 1,2, of analytic functions in the unit disc with f(0) = f' (0) - 1 = 0 satisfying Re [ Dn+1f/ Dnf]<βn for suitable βn > 1 are introduced (D<sup<nf denotes the Ruscheweyh's derivative). The univalence problem for those classes and some integral transformations are considered.


Keywords

Ruscheweyh's Derivative, Univalence, Integral Transformation.
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  • Some Criteria for Univalence in the Unit Disc

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Authors

Milutin Obradovic
Department of Mathematics, University of Belgrade, 4 Karnegieva Street, 11000 Belgrade, Yugoslavia, Serbia

Abstract


The classes Mn, n = 0, 1,2, of analytic functions in the unit disc with f(0) = f' (0) - 1 = 0 satisfying Re [ Dn+1f/ Dnf]<βn for suitable βn > 1 are introduced (D<sup<nf denotes the Ruscheweyh's derivative). The univalence problem for those classes and some integral transformations are considered.


Keywords


Ruscheweyh's Derivative, Univalence, Integral Transformation.