(q1,q2)-quasimetric spaces. Covering mappings and coincidence points. A review of the results
A.V. Arutyunov, А. В. Грешнов
Abstract
In their recent papers, A.V. Arutyunov and A.V. Greshnov introduced (q 1 , q 2 )quasimetric spaces and studied their properties: investigated covering mappings between (q 1 , q 2 )quasimetric spaces, established sufficient conditions for the existence of a coincidence point for two mappings acting between (q 1 , q 2 )-quasimetric spaces such that one is a covering mapping and the other is Lipschitz continuous, proved Banach's fixed point theorem, obtained generalizations for multivalued mappings.The class of (q 1 , q 2 )-quasimetric spaces is sufficiently wide; it includes quasimetric spaces, b-metric spaces, Carnot-Carathodory spaces with Box-quasimetics, Lp-spaces with p (0, 1), etc.The development of the theory of coincidence points of mappings on (q 1 , q 2 )quasimetric spaces initiated interest in the study of more general f -quasimetric spaces and in generalizing Banach's fixed point theorem to such spaces.The present paper is a review of these results.