Preservation of the existence of fixed and coincidence points under homotopy of mappings of ordered sets


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In problems of topology and analysis, well-known theorem on the preservation by any continuous homotopy of the property of a mapping to have a fixed point and the property of a pair of mappings to have a coincidence point are extensively applied. Thus, for contraction mappings and some of their generalizations, Frigon’s results on the preservation of the property to have a fixed point by a homotopy of a special type are known. This paper presents theorems on the preservation by order homotopy of the property of a pair of mappings to have a coincidence point. As a corollary, conditions under which such a homotopy preserves the property of a mapping to have a fixed point are obtained.

作者简介

D. Podoprikhin

Mechanics and Mathematics Faculty

Email: tn-fomenko@yandex.ru
俄罗斯联邦, Moscow, 119991

T. Fomenko

Mechanics and Mathematics Faculty

编辑信件的主要联系方式.
Email: tn-fomenko@yandex.ru
俄罗斯联邦, Moscow, 119991

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