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dc.contributor.authorGrassmann, Eckhardeng
dc.contributor.authorRokne, Joneng
dc.description.abstractLet $S$ be the usual class of univalent functions in {${|z|~<~1}$} normalized by $f(z)~=~z~+$ $sum from i=2 to {inf}$ $a sub i z sup i$ and $V sub n$ the coefficient region of $S$. It is well known that $f$ corresponds to a boundary point of $V sub n$ if and only if $f$ satisfies a quadratic equation of the form $Q(w)dw sup 2~=~R(z)dz sup 2$ called Schiffers equation that maps {${|z|~<~1}$} onto a slit domain. We treat the following problems numerically for $V sub 4$: 1. Given $Q$ find $R$ and $f$. 2. Find the function that maximizes $Re~e sup i sup phi$ $a sub 4$ with theconstraint that $a sub 2$ and $a sub 3$ are some given complex numbers in $V sub 3$. In this case Schiffers equation is a sufficient condition for $f$ to be extremal. The critical trajectories of $Q(w)dw sup 2$ and $R(z)dz sup 2$ are in each case displayed graphically for some particular examples.eng
dc.subjectComputer Scienceeng
dc.publisher.corporateUniversity of Calgaryeng
dc.description.notesWe are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.caeng
dc.identifier.doi Scienceeng

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