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Analytic iteration and differential equations

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Abstract

In this paper we study some mapping properties of analytic iterationsW(a, z). Our purpose is to establish a sufficient condition forW(a, z) to be conformal and univalent inz forz ∈D, whereD is a given domain and for sufficiently small |a |. To this end we consider the differential equationϱW(a, z)/ϱa=L[W(a, z)] with the conditionW(O, z)=z. A sufficient condition for the solutionW(a, z) of this system to be conformal and univalent inD for |a |<a 0 (for somea 0>0), and to satisfy the iteration equation, is established.

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References

  1. L. Bieberbach,Theorie der Gewohnlichen Differentialgliechungen, Springer, Berlin, 1953, p. 1–5.

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  2. P. Erdös and E. Jabotinsky,On analytic iteration, J. Analyse Math.8 (1960–1961), 361–376.

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  3. E. Jabotinsky,On iterational invariants, Technion-Israel Inst. of Tech. Publ.6 (1954–1955), 68–80.

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Author notes

  1. Meira Lavie

    Present address: the Technion-Israel Institute of Technology, Haifa, Israel

Authors and Affiliations

  1. Carnegie Institute of Technology, Pittsburgh, Pennsylvania, U.S.A.

    Meira Lavie

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  1. Meira Lavie
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Additional information

This paper is based on a part of the author’s thesis towards the D.Sc. degree, under the guidance of Professor E. Jabotinsky at the Technion Israel Institute of Technology, Haifa.

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Lavie, M. Analytic iteration and differential equations. Israel J. Math. 5, 86–92 (1967). https://doi.org/10.1007/BF02771626

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  • DOI: https://doi.org/10.1007/BF02771626

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