The Symmetric Versions of Rouché’s Theorem via -Calculus

Raymond Mortini and Rudolf Rupp

Journal of Complex Analysis, 2014, vol. 2014, 1-9

Abstract:

Let be a pair of holomorphic functions. In this expositional paper we apply the -calculus to prove the symmetric version “ on ” as well as the homotopic version of Rouché's theorem for arbitrary planar compacta . Using Eilenberg's representation theorem we also give a converse to the homotopic version. Then we derive two analogs of Rouché's theorem for continuous-holomorphic pairs (a symmetric and a nonsymmetric one). One of the rarely presented properties of the non-symmetric version is that in the fundamental boundary hypothesis, , equality is allowed.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljca:260953

DOI: 10.1155/2014/260953

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