Optics and Spectroscopy (English translation of Optika i Spektroskopiya).
Vol. 103.
2007.
P. 621-628

Covering mappings in metric spaces with fixed points was defined. Two assertions were made including contraction mapping principle and Milyutin's covering mapping theorem. The contraction mapping principle says that if a metric space is complete, any self-mapping of this space satisfying the Lipschitz condition with Lipschitz constant less than 1 has a fixed point. Milyutin's covering mapping theorem says that in case of a normed space and a continuous α-covering mapping where α<0, any mapping satisfying the Lipschitz condition with Lipschitz β <α, the mapping is (α-β) covering. The set valued mapping was said to be α-covering if it satisfies the Milyutin's covering mapping theorem.

Authors

Arutyunov A.V.
^{1}

Journal

Number of issue

2

Language

English

Pages

665-668

Status

Published

Link

Volume

76

Year

2007

Organizations

^{1}Peoples' Friendship University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation

Keywords

Numerical methods; Problem solving; Set theory; Theorem proving; Contraction mapping principle; Lipschitz condition; Metric spaces; Milyutin's covering mapping theorem; Conformal mapping

Date of creation

19.10.2018

Date of change

19.10.2018

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Optics and Spectroscopy (English translation of Optika i Spektroskopiya).
Vol. 103.
2007.
P. 621-628

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