Displaying similar documents to “A fixed point theorem for analytic functions.”

Analytic functions in the unit disc sharing values in a sector

Hong-Yan Xu, Ting-Bin Cao (2012)

Annales Polonici Mathematici

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We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).

Hulls of subsets of the torus in ℂ 2

Herbert Alexander (1998)

Annales de l'institut Fourier

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We construct a non-polynomially convex compact subset of the unit torus in ℂ 2 with polynomially convex hull containing no analytic structure.

Regular analytic transformations of ℝ 2

Joseph Gubeladze (2000)

Annales Polonici Mathematici

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Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of ℝ 2 in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.

A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

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We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.