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Second order differential inequalities in the complex plane

  • II Section Function Theory Of One Complex Variable
  • Conference paper
  • First Online:
Book cover Romanian-Finnish Seminar on Complex Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 743))

Abstract

Let w(z) be regular in the unit disc U and let h(r, s, t) be a complex function defined in a domain of C3. The authors determine conditions on h such that |h(w(z), zw′(z), z2w″(z))| <1 implies |w(z)| <1 and such that Re h(w(z), zw′(z), z2w″(z)) >0 implies Re w(z) >0. Applications of these results to univalent function theory, differential equations and harmonic functions are given.

This work was carried out while the first author was a U.S.A. — Romania Exchange Scholar.

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Bibliography

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Author information

Authors and Affiliations

  1. Department of Mathematics, State University of New York, 14420, Brockport, New York, USA

    Sanford S. Miller

  2. Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

    Petru T. Mocanu

Authors
  1. Sanford S. Miller
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  2. Petru T. Mocanu
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Editor information

Cabiria Andreian Cazacu Aurel Cornea Martin Jurchescu Ion Suciu

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© 1979 Springer-Verlag

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Miller, S.S., Mocanu, P.T. (1979). Second order differential inequalities in the complex plane. In: Cazacu, C.A., Cornea, A., Jurchescu, M., Suciu, I. (eds) Romanian-Finnish Seminar on Complex Analysis. Lecture Notes in Mathematics, vol 743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079503

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  • DOI: https://doi.org/10.1007/BFb0079503

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09550-7

  • Online ISBN: 978-3-540-34861-0

  • eBook Packages: Springer Book Archive

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